Interior Of Saturn Research Articles

Theory of Figures to the Seventh Order and the Interiors of Jupiter and Saturn

Abstract Interior modeling of Jupiter and Saturn has advanced to a state where thousands of models are generated that cover the uncertainty space of many parameters. This approach demands a fast method of computing their gravity field and shape. Moreover, the Cassini mission at Saturn and the ongoing Juno mission delivered gravitational harmonics up to J 12. Here we report the expansion of the theory of figures, which is a fast method for gravity field and shape computation, to the seventh order (ToF7), which allows for computation of up to J 14. We apply three different codes to compare the accuracy using polytropic models. We apply ToF7 to Jupiter and Saturn interior models in conjunction with CMS-19 H/He equation of state. For Jupiter, we find that J 6 is best matched by a transition from an He-depleted to He-enriched envelope at 2–2.5 Mbar. However, the atmospheric metallicity reaches 1 × solar only if the adiabat is perturbed toward lower densities, or if the surface temperature is enhanced by ∼14 K from the Galileo value. Our Saturn models imply a largely homogeneous-in-Z envelope at 1.5–4 × solar atop a small core. Perturbing the adiabat yields metallicity profiles with extended, heavy-element-enriched deep interior (diffuse core) out to 0.4 R Sat, as for Jupiter. Classical models with compact, dilute, or no core are possible as long as the deep interior is enriched in heavy elements. Including a thermal wind fitted to the observed wind speeds, representative Jupiter and Saturn models are consistent with all observed J n values.

Early impact chronology of the icy regular satellites of the outer solar system

The dating of the surfaces of the giant planets' regular satellites is hampered by two issues. The first is the lack of known samples from which radiometric ages can be measured. The second is a potentially different cratering chronology compared to those of the Moon and Mars, due to a difference in the impactor population and planetary system architecture, making a direct comparison and absolute ages derivation difficult. That leaves modelling as the only way to obtain something close to absolute surface ages. Here we applied and reported an improved chronological model of the outer solar system during an episode of dynamical instability caused by giant planet migration. We have combined a series of dynamical and Monte Carlo simulations with various crater scaling laws, impactor size-frequency distributions and observational crater densities to compute the expected crater densities on the surfaces of the regular satellites of Jupiter, Saturn and Uranus. From this, we derived their oldest surface ages. Our impactors are sourced from heliocentric planetesimals that originated from the disk of small bodies exterior to the orbit of the giant planets, and the irregular satellites, which were likely captured by the mutual encounters between the giant planets. With both crater scaling laws and the assumption that the giant planets began their migration at 4.5 Ga, most satellites' surfaces were dated to be older than 4.3 Ga, apart from the inner and small satellites, i.e. Mimas, Enceladus, Hyperion and Miranda. Their estimated surface ages are ca. 4 Ga, although these bodies' masses are expected to have been heavily eroded and if they existed prior to giant planet migration they were likely to be destroyed. Our prediction of old surface ages for the mid-sized Saturnian satellites has implications for their formation, their tidal evolution, the interior of Saturn and the ages of the rings.

The landscape of Saturn’s internal magnetic field from the Cassini Grand Finale

The Cassini mission entered the Grand Finale phase in April 2017 and executed 22.5 highly inclined, close-in orbits around Saturn before diving into the planet on September 15th 2017. Here we present our analysis of the Cassini Grand Finale magnetometer (MAG) dataset, focusing on Saturn’s internal magnetic field. These measurements demonstrate that Saturn’s internal magnetic field is exceptionally axisymmetric, with a dipole tilt less than 0.007 degrees (25.2 arcsecs). Saturn’s magnetic equator was directly measured to be shifted northward by ∼ 0.0468 ± 0.00043 (1σ) RS, 2820±26 km, at cylindrical radial distances between 1.034 and 1.069 RS from the spin-axis. Although almost perfectly axisymmetric, Saturn’s internal magnetic field exhibits features on many characteristic length scales in the latitudinal direction. Examining Br at the a=0.75RS, c=0.6993RS isobaric surface, the degree 4 to 11 contributions correspond to latitudinally banded magnetic perturbations with characteristic width ∼15∘, similar to that of the off-equatorial zonal jets observed in the atmosphere of Saturn. Saturn’s internal magnetic field beyond 60∘, in particular the small-scale features, are less well constrained by the available measurements, mainly due to incomplete spatial coverage in the polar region. Magnetic fields associated with the ionospheric Hall currents were estimated and found to contribute less than 2.5 nT to Gauss coefficients beyond degree 3. The magneto-disk field features orbit-to-orbit variations between 12 nT and 15.4 nT along the close-in part of Grand Finale orbits, offering an opportunity to measure the electromagnetic induction response from the interior of Saturn. A stably stratified layer thicker than 2500 km likely exists above Saturn’s deep dynamo to filter out the non-axisymmetric internal magnetic field. A heat transport mechanism other than pure conduction, e.g. double diffusive convection, must be operating within this layer to be compatible with Saturn’s observed luminosity. The latitudinally banded magnetic perturbations likely arise from a shallow secondary dynamo action with latitudinally banded differential rotation in the semi-conducting layer.

Models of Saturn's Interior Constructed with an Accelerated Concentric Maclaurin Spheroid Method

Abstract The Cassini spacecraft’s Grand Finale orbits provided a unique opportunity to probe Saturn’s gravity field and interior structure. Doppler measurements yielded unexpectedly large values for the gravity harmonics J 6, J 8, and J 10, which cannot be matched using planetary interior models that assume uniform rotation. Instead we present a suite of models that assume the planet’s interior rotates on cylinders, which allows us to match all the observed even gravity harmonics. For every interior model, the gravity field is calculated self-consistently with high precision using the Concentric Maclaurin Spheroid method. We present an acceleration technique for this method, which drastically reduces the computational cost, allows us to efficiently optimize model parameters and map out allowed parameter regions with Monte Carlo sampling, and increases the precision of the calculated J 2n gravity harmonics to match the error bars of the observations, which would be difficult without acceleration. Based on our models, Saturn is predicted to have a dense central core of ∼15–18 Earth masses and an additional 1.5–5 Earth masses of heavy elements in the envelope. Finally, we vary the rotation period in the planet’s deep interior and determine the resulting oblateness, which we compare with the value from radio occultation measurements by the Voyager spacecraft. We predict a rotation period of 10:33:34 hr ± 55 s, which is in agreement with recent estimates derived from ring seismology.

Cassini's Final Year at Saturn: Science Highlights and Discoveries

AbstractScientific findings and new discoveries from the international Cassini‐Huygens mission's exploration of the Saturn system are presented in this special issue of Geophysical Research Letters. In the mission's final year, Cassini dove through the gap between the rings and Saturn for the first time, returning new science in this previously unexplored region. Running low on fuel, Cassini's journey ended on 15 September 2017, as the spacecraft plunged into Saturn's atmosphere and vaporized. Just before the mission concluded, the Grand Finale orbits through the gap provided some of the highest resolution information on Saturn's interior and atmosphere, its rings and inner icy moons, and direct in situ sampling of this intriguing region. Initial results indicate that hydrocarbons appear to be descending into the atmosphere from the rings, that electric currents flow between the inner rings and Saturn, and that a new radiation belt exists in the gap and innermost ring.

Cassini Ring Seismology as a Probe of Saturn’s Interior. I. Rigid Rotation

Abstract Seismology of the gas giants holds the potential to resolve long-standing questions about their internal structure and rotation state. We construct a family of Saturn interior models constrained by the gravity field and compute their adiabatic mode eigenfrequencies and corresponding Lindblad and vertical resonances in Saturn’s C ring, where more than 20 waves with pattern speeds faster than the ring mean motion have been detected and characterized using high-resolution Cassini Visual and Infrared Mapping Spectrometer stellar occultation data. We present identifications of the fundamental modes of Saturn that appear to be the origin of these observed ring waves, and we use their observed pattern speeds and azimuthal wavenumbers to estimate the bulk rotation period of Saturn’s interior to be (median and 5%/95% quantiles), significantly faster than Voyager and Cassini measurements of periods in Saturn’s kilometric radiation, the traditional proxy for Saturn’s bulk rotation period. The global fit does not exhibit any clear systematics indicating strong differential rotation in Saturn’s outer envelope.

Kronoseismology. IV. Six Previously Unidentified Waves in Saturn’s Middle C Ring

Abstract Recent studies of stellar occultations observed by the Visual and Infrared Mapping Spectrometer on board the Cassini spacecraft have demonstrated that multiple spiral wave structures in Saturn’s rings are probably generated by normal-mode oscillations inside the planet. Wavelet-based analyses have been able to unambiguously determine both the number of spiral arms and the rotation rate of many of these patterns. However, there are many more planetary normal modes that should have resonances in the rings, implying that many normal modes do not have sufficiently large amplitudes to generate obvious ring waves. Fortunately, recent advances in wavelet analysis allow weaker wave signals to be uncovered by combining data from multiple occultations. These new analytical tools reveal that a pattern previously identified as a single spiral wave actually consists of two superimposed waves, one with five spiral arms rotating at 1593.°6/day and one with 11 spiral arms rotating at 1450.°5/day. Furthermore, a broad search for new waves revealed four previously unknown wave patterns with six, seven, eight, and nine spiral arms rotating around the planet at 1538.°2/day, 1492.°5/day, 1454.°2/day, and 1421.°8/day, respectively. These six patterns provide precise frequencies for another six fundamental normal modes inside Saturn, yielding what is now a complete sequence of fundamental sectoral normal modes with azimuthal wavenumbers from 2 to 10. These frequencies should place strong constraints on Saturn’s interior structure and rotation rate, while the relative amplitudes of these waves should help clarify how the corresponding normal modes are excited inside the planet.

Phase Curves of Nix and Hydra from the New Horizons Imaging Cameras

Abstract NASA’s New Horizons spacecraft’s voyage through the Pluto system centered on 2015 July 14 provided images of Pluto’s small satellites Nix and Hydra at viewing angles unattainable from Earth. Here, we present solar phase curves of the two largest of Pluto’s small moons, Nix and Hydra, observed by the New Horizons LOng Range Reconnaissance Imager and Multi-spectral Visible Imaging Camera, which reveal the scattering properties of their icy surfaces in visible light. Construction of these solar phase curves enables comparisons between the photometric properties of Pluto’s small moons and those of other icy satellites in the outer solar system. Nix and Hydra have higher visible albedos than those of other resonant Kuiper Belt objects and irregular satellites of the giant planets, but not as high as small satellites of Saturn interior to Titan. Both Nix and Hydra appear to scatter visible light preferentially in the forward direction, unlike most icy satellites in the outer solar system, which are typically backscattering.

Frequency-dependent tidal dissipation in a viscoelastic Saturnian core and expansion of Mimas’ semi-major axis

Regarding tidal dissipation in Saturn, usually parameterized by Saturn's quality factor Q, there remains a discrepancy between conventional estimates and the latest determination that has been derived from astrometric observations of Saturn's inner satellites. If dissipation in Saturn is as large as the astrometric observations suggest, conventional models predict that Mimas' initial orbit should be located inside Saturn's synchronous orbit or even inside its Roche limit. Using simple structure models and assuming Saturn's core to be viscoelastic, we look for dissipation models which are consistent with both the latest astrometric observations and with Mimas' orbital migration. Firstly, using a two-layer model of Saturn's interior structure, we constrain the ranges of rigidity and viscosity of Saturn's core which are consistent with Saturn's dissipation derived from astrometric observations at the tidal frequencies of Enceladus, Tethys, and Dione. Next, within the constrained viscosity and rigidity ranges, we calculate Mimas' semi-major axis considering the frequency dependence of viscoelastic dissipation in Saturn's core. By the two calculations, we evaluate (1) Saturnian models which can explain the astrometrically determined Saturnian dissipation, and (2) whether Mimas' initial semi-major axis is larger than the synchronous orbit. We show that if the core is assumed to be solid with a viscosity of 10^{13}-10^{14} Pa s, the lower boundary of the observed Saturnian dissipation at tidal frequencies of Enceladus, Tethys, and Dione can be explained by our model. In this viscosity range, Mimas can stay outside the synchronous orbit and the Roche limit for 4.5 billion years of evolution. In the case of a frequency dependent viscoelastic dissipative core, the lower boundary of the observed Saturnian dissipation can be consistent with the orbital expansion of Mimas.

New constraints on Saturn's interior from Cassini astrometric data

Using astrometric observations spanning more than a century and including a large set of Cassini data, we determine Saturn's tidal parameters through their current effects on the orbits of the eight main and four coorbital Moons. We have used the latter to make the first determination of Saturn's Love number from observations, k2=0.390±0.024, a value larger than the commonly used theoretical value of 0.341 (Gavrilov & Zharkov, 1977), but compatible with more recent models (Helled & Guillot, 2013) for which the static k2 ranges from 0.355 to 0.382. Depending on the assumed spin for Saturn's interior, the new constraint can lead to a significant reduction in the number of potential models, offering great opportunities to probe the planet's interior. In addition, significant tidal dissipation within Saturn is confirmed (Lainey et al., 2012) corresponding to a high present-day tidal ratio k2/Q=(1.59±0.74)×10−4 and implying fast orbital expansions of the Moons. This high dissipation, with no obvious variations for tidal frequencies corresponding to those of Enceladus and Dione, may be explained by viscous friction in a solid core, implying a core viscosity typically ranging between 1014 and 1016Pa.s (Remus et al., 2012). However, a dissipation increase by one order of magnitude at Rhea's frequency could suggest the existence of an additional, frequency-dependent, dissipation process, possibly from turbulent friction acting on tidal waves in the fluid envelope of Saturn (Ogilvie & Lin, 2004; Fuller et al. 2016).

H/He demixing and the cooling behavior of Saturn

The description of the interior structure and evolution of the Solar System giant planets continues to be a serious challenge. The most prominent example is Saturn for which simple homogeneous evolution models yield ages between 2 and 3 billion years (Gyr), i.e. much shorter than the age of the Solar System of τ⊙=4.56Gyr. It has long been suggested that H/He demixing might occur in the interior of Saturn after the planet has cooled off sufficiently. This incident would mark the begin of an inhomogeneous evolution period in which He droplets sink down and accumulate above the planetary core. The corresponding release of gravitational energy contributes to the intrinsic luminosity of the planet, thereby prolonging its cooling time, perhaps towards the correct value. Such scenarios have been studied in the past on the basis of rather approximate assumptions for the H–He phase diagram. Recently, various ab initio simulations have revealed details of the H–He phase diagram but also of remaining uncertainties (Morales, M.A. et al. [2009]. Proc. Nat. Acad. Sci. USA 106, 1324; Morales, M.A. et al. [2013a]. Phys. Rev. B 87, 174105; Lorenzen, W. et al. [2011]. Phys. Rev. B 84, 235109). In this paper we use the new predictions by Lorenzen et al. and modifications thereof to study the inhomogeneous evolution period of Saturn, with resulting values for the onset of H/He phase separation ts, the cooling time τ, and the atmospheric helium abundance y1. For the planetary interior during the inhomogeneous evolution we assume adiabatic, convective envelopes. We find ts=1Gyr, τ=5.8Gyr, and y1=0.18, while ts≊2Gyr for the Morales et al. data, for which we also estimate τ≈5.1Gyr. On the other hand, reasonable cooling times τ≈τ⊙ are obtained for shifts of the Lorenzen et al. phase diagram by respectively −1300K and +500K, yielding y1=0.22 and y1=0.06. More accurate knowledge of H–He phase diagram is necessary to understand cool gas giant planets. Our results indicate the H–He phase boundaries to occur at slightly higher pressures of Δp≲1Mbar and higher temperatures compared to the predictions by Lorenzen et al., to be tested by future laboratory experiments, for instance by using LH-DACs. However, in addition to the uncertainty of the H–He phase diagram, further effects such as core erosion and non-convective heat transport might strongly influence the planetary structure and evolution. These features may lead to a revision of our assumption of adiabatic envelopes and have to be addressed in future work.

Shocking aluminum into a warm dense state

Physics![Figure][1] Simulation of warm dense matter topology CREDIT: L. B. FLETCHER ET AL. NATURE PHOTONICS 9 (23 MARCH 2015) © NATURE PUBLISHING GROUP In some extreme environments (such as the interior of Saturn, for example), matter is a dense soup of strongly interacting particles: “

Layered convection as the origin of Saturn’s luminosity anomaly

As they keep cooling and contracting, Solar System giant planets radiate more energy than they receive from the Sun. Applying the first and second principles of thermodynamics, one can determine their cooling rate, luminosity, and temperature at a given age. Measurements of Saturn's infrared intrinsic luminosity, however, reveal that this planet is significantly brighter than predicted for its age. This excess luminosity is usually attributed to the immiscibility of helium in the hydrogen-rich envelope, leading to "rains" of helium-rich droplets. Existing evolution calculations, however, suggest that the energy released by this sedimentation process may not be sufficient to resolve the puzzle. Here, we demonstrate using planetary evolution models that the presence of layered convection in Saturn's interior, generated, like in some parts of Earth oceans, by the presence of a compositional gradient, significantly reduces its cooling. It can explain the planet's present luminosity for a wide range of configurations without invoking any additional source of energy. This suggests a revision of the conventional homogeneous adiabatic interior paradigm for giant planets, and questions our ability to assess their heavy element content. This reinforces the possibility for layered convection to help explaining the anomalously large observed radii of extrasolar giant planets.

INTERIOR MODELS OF SATURN: INCLUDING THE UNCERTAINTIES IN SHAPE AND ROTATION

The accurate determination of Saturn's gravitational coefficients by Cassini could provide tighter constraints on Saturn's internal structure. Also, occultation measurements provide important information on the planetary shape which is often not considered in structure models. In this paper we explore how wind velocities and internal rotation affect the planetary shape and the constraints on Saturn's interior. We show that within the geodetic approach the derived physical shape is insensitive to the assumed deep rotation. Saturn's re-derived equatorial and polar radii at 100 mbar are found to be 54,445 ± 10 km and 60,365 ± 10 km, respectively. To determine Saturn's interior, we use one-dimensional three-layer hydrostatic structure models and present two approaches to include the constraints on the shape. These approaches, however, result in only small differences in Saturn's derived composition. The uncertainty in Saturn's rotation period is more significant: with Voyager's 10h39m period, the derived mass of heavy elements in the envelope is 0–7 M⊕. With a rotation period of 10h32m, this value becomes <4 M⊕, below the minimum mass inferred from spectroscopic measurements. Saturn's core mass is found to depend strongly on the pressure at which helium phase separation occurs, and is estimated to be 5–20 M⊕. Lower core masses are possible if the separation occurs deeper than 4 Mbar. We suggest that the analysis of Cassini's radio occultation measurements is crucial to test shape models and could lead to constraints on Saturn's rotation profile and departures from hydrostatic equilibrium.

Can Cassini magnetic field measurements be used to find the rotation period of Saturn's interior?

We investigate the determination of the rotation period of Saturn's interior using magnetic field measurements from Cassini. First, we vary the rotation period and search for the period that yields the smallest rms misfit of a magnetic field model to the data. Second, we search for the period that yields the most power in the non‐axisymmetric components of a magnetic field model. Neither method enables us to determine the rotation period. However, we are able to place a bound on the magnitude of the non‐axisymmetric component of Saturn's magnetic field finding it to be no greater than 4–5% of the axisymmetric component.

Phase separation in hydrogen–helium mixtures at Mbar pressures

The properties of hydrogen-helium mixtures at Mbar pressures and intermediate temperatures (4000 to 10000 K) are calculated with first-principles molecular dynamics simulations. We determine the equation of state as a function of density, temperature, and composition and, using thermodynamic integration, we estimate the Gibbs free energy of mixing, thereby determining the temperature, at a given pressure, when helium becomes insoluble in dense metallic hydrogen. These results are directly relevant to models of the interior structure and evolution of Jovian planets. We find that the temperatures for the demixing of helium and hydrogen are sufficiently high to cross the planetary adiabat of Saturn at pressures approximately 5 Mbar; helium is partially miscible throughout a significant portion of the interior of Saturn, and to a lesser extent in Jupiter.

Empirical models of pressure and density in Saturn's interior: Implications for the helium concentration, its depth dependence, and Saturn's precession rate

We present ‘empirical’ models (pressure vs. density) of Saturn's interior constrained by the gravitational coefficients J 2 , J 4 , and J 6 for different assumed rotation rates of the planet. The empirical pressure–density profile is interpreted in terms of a hydrogen and helium physical equation of state to deduce the hydrogen to helium ratio in Saturn and to constrain the depth dependence of helium and heavy element abundances. The planet's internal structure (pressure vs. density) and composition are found to be insensitive to the assumed rotation rate for periods between 10h:32m:35s and 10h:41m:35s. We find that helium is depleted in the upper envelope, while in the high pressure region ( P ≳ 1 Mbar ) either the helium abundance or the concentration of heavier elements is significantly enhanced. Taking the ratio of hydrogen to helium in Saturn to be solar, we find that the maximum mass of heavy elements in Saturn's interior ranges from ∼6 to 20 M ⊕ . The empirical models of Saturn's interior yield a moment of inertia factor varying from 0.22271 to 0.22599 for rotation periods between 10h:32m:35s and 10h:41m:35s, respectively. A long-term precession rate of about 0.754 ″ yr −1 is found to be consistent with the derived moment of inertia values and assumed rotation rates over the entire range of investigated rotation rates. This suggests that the long-term precession period of Saturn is somewhat shorter than the generally assumed value of 1.77 × 10 6 years inferred from modeling and observations.

Saturn's Gravitational Field, Internal Rotation, and Interior Structure

Saturn's internal rotation period is unknown, though it must be less than 10 hours, 39 minutes, and 22 seconds, as derived from magnetic field plus kilometric radiation data. By using the Cassini spacecraft's gravitational data, along with Pioneer and Voyager radio occultation and wind data, we obtain a rotation period of 10 hours, 32 minutes, and 35 +/- 13 seconds. This more rapid spin implies slower equatorial wind speeds on Saturn than previously assumed, and the winds at higher latitudes flow both east and west, as on Jupiter. Our related Saturn interior model has a molecular-to-metallic hydrogen transition about halfway to the planet's center.

A new spin on Saturn

Measuring the rotation of a gaseous planet is no easy task. For Saturn, do observations of its magnetic field — which indicate that it is spinning more slowly than thought — mark a revolution in our understanding? The absence of a visible solid surface and close alignment of the magnetic field and rotational axis mean that for Saturn, the two best ways of measuring planetary rotation are not available. So Saturn's exact rotation rate is a mystery. The Cassini orbiter provided a detailed map of Saturn's magnetic field, and this has been used to identify an oscillation in the magnetic field with a well-defined period of about 10 hours 47 minutes. The stability of this periodicity over 14 months of observation suggests that it is related to the rotation of Saturn's interior. The nature of the link is not clear, but this is the best estimate yet for Saturn's day length.

Saturn's internal structure and carbon enrichment

We use the clathrate hydrate trapping theory to calculate the enrichments in O, N, S, Xe, Ar and Kr compared to solar in Saturn's atmosphere. For this, we calibrate our calculations using two different carbon abundance determinations that cover the domain of measurements published in recent decades: one derived from the NASA Kuiper Airborne Observatory measurements and the other obtained from the Cassini spacecraft observations. We show that these two carbon abundances imply a different minimum heavy element content for Saturn. Using the Kuiper Airborne Observatory measurement for calibration, the amount of ices accreted by Saturn is found to be consistent with current interior models of this planet. On the other hand, using the Cassini measurement for calibration leads to an ice content in the planet's envelope that is higher than the one derived from the interior models. In this case, reconciling the interior models with the amount of C measured by the Cassini spacecraft requires that significant differential sedimentation of water and volatile species has taken place in Saturn's interior during its lifetime.