The excitation of density and bending waves in Saturn's C ring by planetary oscillation modes presents a unique opportunity to learn about gas giant interiors and rotation. However, theoretical complications related to Saturn's rapid and differential rotation pose a barrier to the full utilization of ring wave detections. We calculate oscillation modes using a complete, non-perturbative treatment of differential rotation modelled after Saturn's zonal winds in self-consistently computed, polytropic equilibria. We find that previous, approximate treatments of the effects of differential rotation in Saturn overestimate shifts in the frequencies of fundamental modes (f-modes) thought to be responsible for the majority of the waves detected in the C ring, due to an omitted modification of the equilibrium shape and structure of the planet by differential rotation. The bias introduced by these frequency overestimates is small, but significant relative to the uncertainties afforded by Cassini data. We additionally consider the non-perturbative effects of Saturn-like differential rotation on the rotational mixing of f-modes and internal gravity modes (g-modes), which is relevant to detections of multiple density waves with very closely split pattern speeds. We find that higher order rotational effects can produce orders-of-magnitude enhancements in the surface gravitational perturbations of g-modes dominated by large spherical harmonic degrees $\ell$, regardless of frequency separation from the sectoral f-mode. Despite this enhancement, we find that the observed fine-splitting of density waves is unlikely to involve g-modes dominated by $\ell\gtrsim 10$. This restriction may aid in the inference of possible internal structures for Saturn.
Saturn's Evolutionary History and Seismology: Survival of Deep Stably Stratified Regions in Evolutionary Models of Saturn Consistent with Ring Seismology
Princeton University（普林斯顿大学）；Canadian Institute for Theoretical Astrophysics, University of Toronto（多伦多大学加拿大理论天体物理研究所）；University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；University of California Los Angeles（加州大学洛杉矶分校）
Normal mode oscillations in Saturn excite density and bending waves in the C Ring, providing a valuable window into the planet's interior. Saturn's fundamental modes (f modes) excite the majority of the observed waves, while gravito-inertial modes (rotationally modified g modes) associated with stable stratification in the deep interior provide a compelling explanation for additional density waves with low azimuthal wavenumbers m. However, multiplets of density waves with nearly degenerate frequencies, including an m=3 triplet, still lack a definitive explanation. We investigate the effects of…
Brown dwarfs and directly imaged giant planets exhibit significant evidence for active atmospheric circulation, which induces a large-scale patchiness in the cloud structure that evolves significantly over time, as evidenced by infrared light curves and Doppler maps. These observations raise critical questions about the fundamental nature of the circulation, its time variability, and the overall relationship to the circulation on Jupiter and Saturn. Jupiter and Saturn themselves exhibit numerous robust zonal (east-west) jet streams at the cloud level; moreover, both planets exhibit long-term s…
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 twenty waves with pattern speeds faster than the ring mean motion have been detected and characterized using high-resolution Cassini Visual and Infrared Mapping Spectrometer (VIMS) stellar occultation data. We present identifications of the fundam…
The best constraints on the internal structures of giant planets have historically come from measurements of their gravity fields. These gravity data are inherently mostly sensitive to a planet's outer regions, providing only loose constraints on the deep interiors of Jupiter and Saturn. This fundamental limitation stymies efforts to measure the mass and compactness of these planets' cores, crucial properties for understanding their formation pathways and evolution. However, studies of Saturn's rings have revealed waves driven by pulsation modes within Saturn, offering independent seismic prob…
The fluid dynamics in planet Saturn gives rise to alternating east-west jet streams, large cyclonic and anticyclonic vortices, and a dipole-dominant magnetic field which is highly axisymmetric about the planetary rotation axis. Modelling these features in a self-consistent manner is crucial for understanding the dynamics of Saturn's interior and atmosphere. Here we report a turbulent high-resolution dynamo simulation in a spherical shell which produces these features simultaneously for the first time. A crucial model ingredient is a long-hypothesised stably stratified layer (SSL), sandwiched b…
As it has already done for Earth, the sun, and the stars, seismology has the potential to radically change the way the interiors of giant planets are studied. In a sequence of events foreseen by only a few, observations of Saturn's rings by the Cassini spacecraft have rapidly broken ground on giant planet seismology. Gravity directly couples the planet's normal mode oscillations to the orbits of ring particles, generating spiral waves whose frequencies encode Saturn's internal structure and rotation. These modes have revealed a stably stratified region near Saturn's center, and provided a new …
Normal mode seismology is a promising means of measuring rotation in gas giant interiors, and ring seismology presents a singular opportunity to do so at Saturn. We calculate Saturn's normal modes of oscillation and zonal gravity field, using nonperturbative methods for normal modes in the rigidly rotating approximation, and perturbative methods for the shifts that Saturn's deep winds induce in the mode frequencies and zonal gravity harmonics. The latter are calculated by solving the thermo-gravitational wind equation in an oblate geometry. Comparing many such models to gravity data and the fr…
During the past few years, both the Cassini mission at Saturn and the Juno mission at Jupiter, provided measurements with unprecedented accuracy of the gravity and magnetic fields of the two gas giants. Using the gravity measurements, it was found that the strong zonal flows observed at the cloud-level of the gas giants are likely to extend thousands of kilometers deep into the planetary interior. However, the gravity measurements alone, which are by definition an integrative measure of mass, cannot constrain with high certainty the exact vertical structure of the flow. Taking into account the…
安德森和舒伯特（Anderson & Schubert，2007，Science，317，1384）提出，土星的自转周期可以通过最小化100毫巴等值面相对于大地水准面的动态高度来确定;他们得出的自转周期为10小时32分35秒。我们调查同样的方法，木星，看看木星的旋转周期是通过最大限度地减少其等压面（1巴的压力水平）的动态高度使用纬向风数据预测。发现木星和土星的自转周期为9 h 54 m 29 s.进一步，我们研究了用先锋号和旅行者号的掩星半径拟合木星和土星的最小化方法. 9小时55米30秒和10小时32米35秒的旋转周期被发现，以最小化的动力学高度木星和土星，分别。虽然没有动力学原理要求等压面的动力学高度最小化，但该方法在木星上的成功应用支持了它与土星的相关性。利用平衡理论导出了木星和土星的自转周期，得到了木星和土星的自转周期分别为9 h 55 m 20 s和10 h 31 m 49 s。我们表明，木星和土星的形状可以使用固体旋转，这表明纬向风有轻微的影响，这两颗行星的行星形状。不同方法预测的土星自转周期值的一致性支持了土星自转周期约为10 h 32 m的结论。
We examine Saturn's atmosphere with observations from ground-based telescopes and Hubble Space Telescope (HST). We present a detailed analysis of observations acquired during 2018. A system of polar storms that appeared in the planet in March 2018 and remained active with a complex phenomenology at least until Sept. is analyzed elsewhere (Sanchez-Lavega et al., in press , 2019). Many of the cloud features in 2018 are long-lived and can be identified in images in 2017, and in some cases, for up to a decade using also Cassini ISS images. Without considering the polar storms, the most interesting…
The nature and structure of the observed east-west flows on Jupiter and Saturn has been one of the longest-lasting mysteries in planetary science. This mystery has been recently unraveled due to the accurate gravity measurements provided by the Juno mission to Jupiter and the Grand Finale of the Cassini mission to Saturn. These two experiments, which coincidentally happened around the same time, allowed determination of the vertical and meridional profiles of the zonal flows on both planets. This paper reviews the topic of zonal jets on the gas giants in light of the new data from these two ex…
How deep do Saturn's zonal winds penetrate below the cloud-level has been a decades-long question, with important implications not only for the atmospheric dynamics, but also for the interior density structure, composition, magnetic field and core mass. The Cassini Grand Finale gravity experiment enables answering this question for the first time, with the premise that the planet's gravity harmonics are affected not only by the rigid body density structure but also by its flow field. Using a wide range of rigid body interior models and an adjoint based thermal wind balance, we calculate the op…
The recent gravity field measurements of Jupiter (Juno) and Saturn (Cassini) confirm the existence of deep zonal flows reaching to a depth of 5\% and 15\% of the respective radius. Relating the zonal wind induced density perturbations to the gravity moments has become a major tool to characterise the interior dynamics of gas giants. Previous studies differ with respect to the assumptions made on how the wind velocity relates to density anomalies, on the functional form of its decay with depth, and on the continuity of antisymmetric winds across the equatorial plane. Most of the suggested verti…
We analyze the range rate residual data from Cassini's gravity experiment that cannot be explained with a static, zonally symmetric gravity field. In this paper we reproduce the data using a simple forward model of gravity perturbations from normal modes. To do this, we stack data from multiple flybys to improve sensitivity. We find a partially degenerate set of normal mode energy spectra which successfully reproduce the unknown gravity signal from Cassini's flybys. Although there is no unique solution, we find that the models most likely to fit the data are dominated by gravitational contribu…
Recent precise measurements at Jupiter's and Saturn's gravity fields constrain the properties of the zonal flows in the outer envelopes of these planets. A simplified dynamic equation, sometimes called the thermal wind or thermo-gravitational wind equation, establishes a link between zonal flows and the related buoyancy perturbation, which in turn can be exploited to yield the dynamic gravity perturbation. Whether or not the action of the dynamic gravity perturbation needs to be explicitly included in this equation, an effect we call the Dynamic Self Gravity (DSG), has been a matter of intense…
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 that cannot be matched with 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…
Since the 1950s, quasi-periodic oscillations have been studied in the terrestrial equatorial stratosphere. Other planets of the solar system present (or are expected to present) such oscillations, like the Jupiter Equatorial Oscillation(JEO) and the Saturn Semi-Annual Oscillation (SSAO). In Jupiter's stratosphere, the equatorial oscillation of its relative temperature structure about the equator, is characterized by a quasi-period of 4.4 years. The stratospheric wind field in Jupiter's equatorial zone has never been directly observed. In this paper, we aim at mapping the absolute wind speeds i…
Observations of planets throughout our Solar System have revealed that the Earth is not alone in possessing natural, inter-annual atmospheric cycles. The equatorial middle atmospheres of the Earth, Jupiter and Saturn all exhibit a remarkably similar phenomenon - a vertical, cyclic pattern of alternating temperatures and zonal (east-west) wind regimes that propagate slowly downwards with a well-defined multi-Earth-year period. Earth's Quasi-Biennial Oscillation (QBO, observed in the lower stratospheres with an average period of 28 months) is one of the most regular, repeatable cycles exhibited …
The Composite InfraRed Spectrometer (CIRS) on board Cassini revealed an equatorial oscillation of stratospheric temperature, reminiscent of the Earth's Quasi-Biennial Oscillation (QBO), as well as anomalously high temperatures under Saturn's rings. To better understand these predominant features of Saturn's atmospheric circulation in the stratosphere, we have extended towards higher altitudes the DYNAMICO-Saturn global climate model (GCM), already used in a previous publication to study the tropospheric dynamics, jets formation and planetary-scale waves activity. Firstly, we study the higher m…
Excitation and Damping of Oscillation Modes in Gaseous Planets
California Institute of Technology（加州理工学院）；Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；New Mexico State University（新墨西哥州立大学）
Similar to Earth, Saturn's largest moon, Titan, possesses a system of high-altitude zonal winds (or jets) that encircle the globe. Using the Atacama Large Millimeter/submillimeter Array (ALMA) in August 2016, Lellouch et al. (2019) discovered an equatorial jet at much higher altitudes than previously known, with a surprisingly fast speed of up to ~340 m/s, but the origin of such high velocities is not yet understood. We obtained spectrally and spatially resolved ALMA observations in May 2017 to map Titan's 3D global wind field and compare our results with a reanalysis of the August 2016 data. …
