DDA 2015 – Recent dynamical evolution of Mimas and Enceladus

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Session: Moon Formation and Dynamics III

Maja Cuk (SETI Institute)

Abstract

Mimas and Enceladus are the smallest and innermost mid-sized icy moons of Saturn. They are each caught in a 2:1 orbital resonance with an outer, larger moon: Mimas with Tethys, Enceladus with Dione. This is where the similarities end. Mimas is heavily cratered and appears geologically inactive, while Enceladus has a young surface and high tidal heat flow. Large free eccentricity of Mimas implies low tidal dissipation, while Enceladus appears very dissipative, likely due to an internal ocean. Their resonances are very different too. Mimas is caught in a 4:2 inclination type resonance with Tethys which involves inclinations of both moons. Enceladus is in a 2:1 resonance with Dione which affects only Enceladus’s eccentricity. The well-known controversy over the heat flow of Enceladus can be solved by invoking a faster tidal evolution rate than previously expected (Lainey et al. 2012), but other mysteries remain. It has been long known that Mimas has very low probability of being captured into the present resonance, assuming that the large resonant libration amplitude reflects sizable pre-capture inclination of Mimas. Furthermore, Enceladus seems to have avoided capture into a number of sub-resonances that should have preceded the present one. An order of magnitude increase in the rate of tidal evolution does not solve these problems. It may be the time to reconsider the dominance of tides in the establishment of these resonances, especially if the moons themselves may be relatively young. An even faster orbital evolution due to ring/disk torques can help avoid capture into smaller resonances. Additionally, past interaction of Mimas with Janus and Epimetheus produce some of the peculiarities of Mimas’ current orbit. At the meeting I will present numerical integrations that confirm the the existence of these problems, and demonstrate the proposed solutions.

Notes

  • tidal rates $\dfrac{1}{a}\dfrac{d a}{d t}$: Mimas = 59, Enceladus = 23
  • numerical integrations — brute force
    • artificial migration
    • slow
  • the trouble with Mimas
    • Mimas and Tethys in inclination-type 4:2 MMR
    • inclination of both moons affected by the resonance
    • libration amp. of resonance is large, ~100 deg $\rightarrow$ primordial Mimas inclination — doesn’t work
    • eccentricity of Tethys has complex effects
    • Mimas-Tethys evolution rate: $\dfrac{da_{moon}}{dt} \propto \dfrac{R^5_{planet}}{a^{3/2}}$
  • introduce ad hoc ring torques — artificial torque on Prometheus
    • gives Tethys resonance a kick
    • $\therefore$ don’t take Mimas-Tethys resonance too seriously
  • …more ad hoc games…
  • rings-Janus-Mimas-Enceladus-Dione system evolution is very complex

DDA 2015 – Rotational and interior models for Enceladus II

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Radwan Tajeddine (Cornell)

Abstract

We will discuss the underlying dynamical models and the consequent interior models that pertain to our discovery of a forced rotational libration for Saturn’s moon Enceladus (Thomas et al. 2015).

Despite orbital variations that change the mean motion on timescales of several years owing to mutual satellite interactions, the rotation state of Enceladus should remain synchronous with the varying mean motion, as long as damping is as expected (Tiscareno et al. 2009, Icarus). Taking that dynamically synchronous rotation as the ground state, we construct a model that naturally focuses on the physically interesting librations about the synchronous state that occur on orbital timescales. We will discuss the differences between the method used here and other dynamical methods (e.g., Rambaux et al. 2010, GRL; cf. Tajeddine et al. 2014, Science), and we will review the rotation states (whether known or predicted) of other moons of Saturn.

We will also describe our measurements of the control point network on the surface of Enceladus using Cassini images, which was then used to obtain its physical forced libration amplitude at the orbital frequency. The fit of Cassini data results in a libration amplitude too large to be consistent with a rigid connection between the surface and the core, ruling out the simplest interior models (e.g., homogeneous, two-layer, two-layer with south polar anomaly). Alternatively, we suggest an interior model of Enceladus involving a global ocean that decouples the shell from the core, with a thinner icy layer in the south polar region as an explanation for both the libration (Thomas et al. 2015) and the gravity (Iess et al. 2014, Science) measurements.

Notes

  • Libration measurement
    • 3D reconstruction of coords of a network of control point (fiducial satellite surface points — e.g. craters)
    • most of Enceladus’s orbit was covered
    • Thomas et al. 2015
    • minimize RMS residual $\rightarrow 0.120 \pm 0.014$ deg
  • Solid models
    • core plus two-layer in hydro.equilib. plus south polar sea
      • measured libration amplitude rules this out
    • decoupled shell from the core (indep.librations)
      • consistent with observed libration amplitude if shell thickness 21-26 km and ocean thickness 26-31 km
  • Gravity data
    • suggests a local mass anomaly — interpreted as ocean thicker under south pole

DDA 2015 – Rotational and interior models for Enceladus I

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Session: Moon Formation and Dynamics II

Matthew S. Tiscareno (Cornell)

Abstract

We will discuss the underlying dynamical models and the consequent interior models that pertain to our discovery of a forced rotational libration for Saturn’s moon Enceladus (Thomas et al. 2015).

Despite orbital variations that change the mean motion on timescales of several years owing to mutual satellite interactions, the rotation state of Enceladus should remain synchronous with the varying mean motion, as long as damping is as expected (Tiscareno et al. 2009, Icarus). Taking that dynamically synchronous rotation as the ground state, we construct a model that naturally focuses on the physically interesting librations about the synchronous state that occur on orbital timescales. We will discuss the differences between the method used here and other dynamical methods (e.g., Rambaux et al. 2010, GRL; cf. Tajeddine et al. 2014, Science), and we will review the rotation states (whether known or predicted) of other moons of Saturn.

We will also describe our measurements of the control point network on the surface of Enceladus using Cassini images, which was then used to obtain its physical forced libration amplitude at the orbital frequency. The fit of Cassini data results in a libration amplitude too large to be consistent with a rigid connection between the surface and the core, ruling out the simplest interior models (e.g., homogeneous, two-layer, two-layer with south polar anomaly). Alternatively, we suggest an interior model of Enceladus involving a global ocean that decouples the shell from the core, with a thinner icy layer in the south polar region as an explanation for both the libration (Thomas et al. 2015) and the gravity (Iess et al. 2014, Science) measurements.

Notes

  • Enceladus
    • 2nd largest Saturnian moon
    • Plumes — salty jets — observed by Cassini
    • What is under the surface?
    • Rotational parameters $\rightarrow$ interior structure
  • Forcedlibrations
    • same period as orbital
    • nat. freq. $\omega_0 \approx n \sqrt{3 (B-A)/C}$
    • near-spherical: moon always points at empty focus (synchronous)
    • elongated: moon would always point at Saturn
    • Enceladus axis oscillates around empty focus (synchronous rotation)
    • as $\dfrac{B-A}{C} \rightarrow \dfrac{1}{3}$, resonance (Tiscareno et al. 2009)
    • but Enceladus $\dfrac{B-A}{C} \ll \dfrac{1}{3}$
      • Enceladus libration $0.120\pm0.014$ deg
      • rules out rigid connection between surface and core
      • hence, some kind of global subsurface ocean
  • Mean motion variations
    • Enceladus resonant arguments from interaction with Dione:
      $ILR_D = \lambda_E\, – 2 \lambda_D + \varpi_E$ (librating)
      $CIR_D = \lambda_E\, – 2 \lambda_D + \Omega_D$ (circulating)
      $CER_D = \lambda_E\, – 2 \lambda_D + \varpi_D$ (circulating)
    • As long as damping is sufficiently strong, synchronous rotation maintained
      • damping must be $\gamma_{\pi/2} = \dfrac{2 e}{1\, – \left(\dfrac{n}{\omega_0}\right)^2} \Rightarrow \tau \approx 1.0\,Q\ \mathrm{days}$
      • but $10 \lt Q \lt 100$ days
    • rot. rate varies with the CER and ILR freqs
      • not really “librations”
      • maintaining synch. rot., while the mean motion varies quasiperiodically
  • Rotational models
    • Global Fourier components have limited usefulness
    • MM variation more complex than a few periodic terms
    • Define rot.statewrt Saturn
      • base state: synch rot (expected for low triaxiality)
      • accounts for MM variation
      • easy to generate a range of kernels for many vals of $\gamma$
    • Tiscareno 2015
    • deflect $\psi(t) = (2 e+\gamma)\sin M$
    • generate kernels of $\psi(t)$ for a wide range of $\gamma$ values, check for best control-point resids
    • dissipation?