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Register a new userConstraining Saturns interior with ring seismology: effects of differential rotation and stable stratification
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Normal mode oscillations in Saturn excite density and bending waves in the C Ring, providing a valuable window into the planets interior. Saturns 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 rapid and differential rotation on Saturns oscillations, calculating normal modes for independently constrained interior models. We use a non-perturbative treatment of rotation that captures the full effects of the Coriolis and centrifugal forces, and consequently the mixing of sectoral f modes with g modes characterized by very different spherical harmonic degrees. Realistic profiles for differential rotation associated with Saturns zonal winds can enhance these mode interactions, producing detectable oscillations with frequencies separated by less than 1%. Our calculations demonstrate that a three-mode interaction involving an f mode and two g modes can feasibly explain the finely split m=3 triplet, although the fine-tuning required to produce such an interaction generally worsens agreement with seismological constraints provided by m=2 density waves. Our calculations additionally demonstrate that sectoral f mode frequencies are measurably sensitive to differential rotation in Saturns convective envelope. Finally, we find that including realistic equatorial antisymmetry in Saturns differential rotation profile couples modes with even and odd equatorial parity, producing oscillations that could in principle excite both density and bending waves simultaneously.
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Using astrometric observations spanning more than a century and including a large set of Cassini data, we determine Saturns 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 Saturns Love number, $k_2=0.390 pm 0.024$, 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 $k_2$ ranges from 0.355 to 0.382. Depending on the assumed spin for Saturns interior, the new constraint can lead to a reduction of up to 80% in the number of potential models, offering great opportunities to probe the planets interior. In addition, significant tidal dissipation within Saturn is confirmed (Lainey et al., 2012) corresponding to a high present-day tidal ratio $k_2/Q=(1.59 pm 0.74) times 10^{-4}$ 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 $10^{14}$ and $10^{16}$ Pa.s (Remus et al., 2012). However, a dissipation increase by one order of magnitude at Rheas 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 & Li, 2004). Alternatively, a few of Saturns moons might themselves experience large tidal dissipation.
In previous work we identified six Sun-like stars observed by Kepler with exceptionally clear asteroseismic signatures of rotation. Here, we show that five of these stars exhibit surface variability suitable for measuring rotation. In order to further constrain differential rotation, we compare the rotation periods obtained from light-curve variability with those from asteroseismology. The two rotation measurement methods are found to agree within uncertainties, suggesting that radial differential rotation is weak, as is the case for the Sun. Furthermore, we find significant discrepancies between ages from asteroseismology and from three different gyrochronology relations, implying that stellar age estimation is problematic even for Sun-like stars.
Saturns ionosphere is produced when the otherwise neutral atmosphere is exposed to a flow of energetic charged particles or solar radiation. At low latitudes the latter should result in a weak planet-wide glow in infrared (IR), corresponding to the planets uniform illumination by the Sun. The observed low-latitude ionospheric electron density is lower and the temperature higher than predicted by models. A planet-ring magnetic connection has been previously suggested in which an influx of water from the rings could explain the lower than expected electron densities in Saturns atmosphere. Here we report the detection of a pattern of features, extending across a broad latitude band from ~25 to 60 degrees, that is superposed on the lower latitude background glow, with peaks in emission that map along the planets magnetic field lines to gaps in Saturns rings. This pattern implies the transfer of charged water products from the ring-plane to the ionosphere, revealing the influx on a global scale, flooding between 30 to 43% of the planets upper-atmospheric surface. This ring `rain plays a fundamental role in modulating ionospheric emissions and suppressing electron densities.
In this paper, we introduce a simplified model to understand the location of Saturns F ring. The model is a planar restricted five-body problem defined by the gravitational field of Saturn, including its second zonal harmonic $J_2$, the shepherd moons Prometheus and Pandora, and Titan. We compute accurate long-time numerical integrations of (about 2.5 million) non-interacting test-particles initially located in the region between the orbits of Prometheus and Pandora, and address whether they escape or remain trapped in this region. We obtain a wide region of initial conditions of the test particles that remain confined. We consider a dynamical stability indicator for the test particles motion defined by computing the ratio of the standard deviation over the average value of relevant dynamical quantities, in particular, for the mean-motion and the semi-major axis. This indicator separates clearly a subset of trapped initial conditions that appear as very localized stripes in the initial semi-major axis and eccentricity space for the most stable orbits. Retaining only these test particles, we obtain a narrow eccentric ring which displays sharp edges and collective alignment. The semi-major axis of the accumulation stripes of the stable ring-particles can be associated with resonances, mostly involving Prometheus outer Lindblad and co-rotation resonances, but not exclusively. Pandoras inner Lindblad and co-rotation resonances as well as low-order three-body resonances typically coincide with gaps, i.e., regions of instabilities. Comparison of our results with the nominal data for the F ring shows some correspondence.
The $mu$ and $ u$ rings of Uranus form a secondary ring-moon system with the satellites Puck, Mab,Portia, and Rosalind. These rings are tenuous and dominated by micrometric particles, which can be strongly disturbed by the solar radiation pressure. We performed a numerical analysis of the orbital evolution of a sample of particles under the influence of the solar radiation force and the planetary oblateness, combined with the gravitational interaction with the close satellites. The most likely result is a collisions and the deposition of particles onto the surface of these satellites. Since this mechanism tends to cause a depletion of material of the rings, we investigate additional sources for these dust particles. Adopting a rough estimative of the flux of interplanetary meteoroids, we found that the ejections from Mab could generate a ring with optical depth comparable with the observations. A similar analysis was carried out for the F-ring dust band. The damping due to the Saturns oblateness prevents the overstated changes of the eccentricity and increases in the lifetime of the particles. Therewithal photometric study of the F-ring using Cassini images revealed that substantial secular increase in the brightness of Saturns F ring has occurred in the last 25 years. The shapes of the phase curves from Cassini and Voyager are similar, suggesting that although the number of dust particles has increased, the overall distribution of sizes is unchanged. The dust bands that permeate the rings of Uranus were observed late in 2007 during the equinox, when the Sun crossed the ring plane. Images taken with the VLT were processed and then combined to result in long-exposure frames. For each frame, the north and south radial profiles were extracted. They will be used to develop a photometric model.
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