Juno & Jupiter's gravity field

• Juno will measure Jupiter's composition, gravity field, magnetic field, and polar magnetosphere.

• External gravitational potential of rotating body:

$V(r, \theta) = \frac{GM}{r} \left[ 1- \sum_{n=1} J_{2n} \left(\frac{a}{r}\right)^{2n} P_{2n} (\cos{\theta}) \right]$

$J_{2n}$: gravitational moments (zonal harmonic coefficients);

$P_{2n}$: Legendre polynomial;

$\theta$: angle to the rotational axis.

2016-2021

Jupiter's gravitational moments

• Even harmonics probe the shape and density distribution.
• Odd harmonics probe the dynamical processes that are not north-south symmetric.

Image credit: James Tuttle Keane

Kaspi et al. (2020)

Infer Jupiter's deep interior

• Higher harmonics probe the outer regions of the planet;
• If the outer regions are constrained by other measurements, then higher harmonics can probe the deep interior (i.e., core region).

Galileo satellite

Galileo entry probe

Image credit: NASA

Jupiter interior model

• Why 3 layers instead of 2 layers?
• Why diffuse core instead of compact core?

Image credit: Stevenson (2020)

Jupiter's two-layered atmosphere

Image credit: Marley & Fortney, Encyclopedia of the Solar System

Jupiter's two-layered atmosphere

Image credit: Marley & Fortney, Encyclopedia of the Solar System

"Helium rain"

(Stevenson & Salpeter, 1977a, b)

Image credit: Hubbard & Militzer (2016)

Jupiter interior model

• Hydrostatic equilibrium

$$\nabla P = \rho \nabla (V_g+V_{cf})$$

• Gravitational potential $V_g$
• Centrifugal potential: $V_{cf}$
• Isentropic equation of state: $$P=P(\rho)$$

Jupiter dilute core

Wahl et al. (2017)

A more "realistic" model:

4-layer model

Debras & Chabrier (2019)

Image credit: Stevenson (2020)

Summary

• Inferring Jupiter interior from gravity measurements
  • Higher harmonics probe outer surface;
  • Juno's gravity measurements & Galileo's surface layer constraint --> core property
• Model of Jupiter interior
  • Envelope: at least 2 layers because of He rain;
  • Dilute core