Jupiter dilute core
Wei Zhu (祝伟)
Thursday group meeting
2020-07-09
Papers presenting dilute core models: Wahl et al. (2017); Debras & Chabrier (2019)
A recent review on Jupiter: Stevenson (2020)
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
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
Immiscible liquid: oil on up of water
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: $$ P=P(\rho) $$
molecular layer
metallic layer
different entropy
Jupiter dilute core
"standard" model
A dilute core is preferred, in addition to an enhanced entropy offset or a reduced molecular layer metallicity (less likely).
A more "realistic" model:
4-layer model
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