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)


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.


  • 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?

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