May 2024
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23 Reads
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3 Citations
Science Advances
One of the stranger planetary rings is Saturn’s narrow, clumpy F ring, lying just outside the main rings, in a region disturbed by chaotic orbital dynamics. We show that the F ring has a stable “true core” that dominates its mass and is confined into discontinuous short arcs of particles larger than a few millimeters in radius. The more obvious micron-size particles seen in images, outlining and obscuring the true core, contribute only a small fraction of its mass. We found that these arcs of large particles orbit Saturn in a specific corotational resonance with the nearby 100-kilometer diameter ringmoon Prometheus, which stabilizes the F ring material and allows it to persist within the disturbed region for decades or longer. Toward the end of the observing period, a small chaotic glitch in the orbit of Prometheus temporarily disrupted the confinement, but the arcs seem to be able to adapt.
![Cartoon showing a tidally distorted planet of mass Mp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M_{\mathrm{p}}$\end{document} and radius Rp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R_{\mathrm{p}}$\end{document}, due to a moon of mass Mm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$M_{\mathrm{m}}$\end{document} at semi-major axis am\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$a_{\mathrm{m}}$\end{document}. The planet’s spin frequency is Ωp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega _{\mathrm{p}}$\end{document} and the moon’s orbital frequency is Ωm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega _{\mathrm{m}}$\end{document}. The tidal quality factor of the planet, Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Q$\end{document}, can be visualized as a lag angle of δ=1/Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\delta = 1/Q$\end{document} between the tidal bulge and the moon’s position. In reality, the effective value of Q\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Q$\end{document} can involve more complicated tidal distortion within the planet due to dynamical tides](https://www.researchgate.net/publication/378338895/figure/fig1/AS:11431281230344962@1710904558681/Cartoon-showing-a-tidally-distorted-planet-of-mass-Mpdocumentclass12ptminimal_Q320.jpg)
![Slices of the internal structures of Jupiter, Saturn, Uranus and Neptune highlighting compositional gradients in helium (orange) and heavy elements (blue). Jupiter and Saturn are characterized by a phase separation of helium in metallic hydrogen starting near Mbar pressures. Juno and Cassini measurements also indicate the presence of a dilute heavy element core in these planets, implying that heavy elements are partially mixed with hydrogen and helium rather forming separate pure layers. In this diagram, each layer corresponds to a 2% increase of the helium/hydrogen ratio (orange) or of the heavy element mass fraction Z\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Z$\end{document} (blue). For Uranus and Neptune, a structure dominated by well-separated layers, including a solid superionic water layer, is presented. However, solutions with compositions that evolve more continuously are also highly plausible. Image reproduced with permission from Guillot et al. (2023), copyright by ASP](https://www.researchgate.net/publication/378338895/figure/fig2/AS:11431281230372352@1710904558902/Slices-of-the-internal-structures-of-Jupiter-Saturn-Uranus-and-Neptune-highlighting_Q320.jpg)
![Phase diagrams of key elements with pressure-temperature profiles of relevant astrophysical objects (the Sun, brown dwarfs CoRoT-15b and Gl229 B, giant exoplanet HD 209458 b, and Jupiter, Saturn, Uranus and Neptune). Pressures are in bars (1 bar=105 Pa=106 dyn/cm2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1\text{ bar}=10^{5}\text{ Pa}=10^{6}\text{ dyn/cm}^{2}$\end{document}). (a): Location of the hydrogen-helium phase separation leading to helium rain-out in Jupiter and Saturn (yellow). The critical demixing temperatures obtained from ab-initio simulations are shown in orange. Those obtained from high-pressure experiments are shown as two triangles connected by a red curve. (b): Phase diagram of H2O, including the fluid molecular, ionic and plasma phases, the solid ice phases and the superionic phase, as labelled. (c): Region of iron solidification, relevant for the central regions of Jupiter and possibly Saturn. (d): Regions of silicate solidification, relevant in the interiors of Uranus, Neptune, Saturn and Jupiter. Note that MgSiO3 decomposes at high pressures into MgO (which should be solid in Jupiter and Saturn) and SiO2 (which may still be liquid in the deep interior of Jupiter and Saturn). Image reproduced with permission from Guillot et al. (2023), copyright by ASP; see references therein](https://www.researchgate.net/publication/378338895/figure/fig3/AS:11431281230372353@1710904559227/Phase-diagrams-of-key-elements-with-pressure-temperature-profiles-of-relevant_Q320.jpg)
![Estimates of static stability in Jupiter’s atmosphere as measured from its Brünt-Väisälä frequency N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$N$\end{document}. Shaded bars (to the left of the dashed line) are from measurements and models of Jupiter’s vertical structure; black and white bars (to the right of the dashed line) are for vortex surroundings as determined by numerical models of the Great Red Spot, and of Jupiter’s anticyclones. Image reproduced with permission from Wong et al. (2011), copyright by Elsevier](https://www.researchgate.net/publication/378338895/figure/fig4/AS:11431281230372354@1710904559474/Estimates-of-static-stability-in-Jupiters-atmosphere-as-measured-from-its-Bruent-Vaeisaelae_Q320.jpg)
![Type of waves constituting the dynamical tide in fluid planetary layers. We introduce their characteristic frequencies: the Alfvén frequency ωA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega _{\mathrm{A}}$\end{document}, where k→\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vec{k}$\end{document} is the wave vector and V→A=B→/μ0ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\vec{V}}_{\mathrm{A}}={\vec{B}}/\sqrt{\mu _{0}\rho}$\end{document} is the Alfvén velocity (B→\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vec{B}$\end{document} being the magnetic field, ρ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\rho $\end{document} the density, μ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mu _{0}$\end{document} the vacuum permeability), the inertial frequency 2Ωp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$2\Omega _{\mathrm{p}}$\end{document} (Ωp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\Omega _{\mathrm{p}}$\end{document} being the angular velocity of the planet), the Brünt-Väisälä frequency N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$N$\end{document} defined in Eq. (1), and the Lamb frequency fL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f_{\mathrm{L}}$\end{document}. For tidally excited waves in stably stratified regions of giant planets, we typically expect ωA<2Ωp<N<fL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\omega _{\mathrm{A}} < 2 \Omega _{\mathrm{p}} < N < f_{\mathrm{L}}$\end{document}, but this may not always be true. Image adapted from Mathis and de Brye (2011)](https://www.researchgate.net/publication/378338895/figure/fig5/AS:11431281230372355@1710904559634/Type-of-waves-constituting-the-dynamical-tide-in-fluid-planetary-layers-We-introduce_Q320.jpg)
