Does this planet have a rock/ice core?
Nancy Morrison
Bag Lunch Jan. 21, 2003
Does Jupiter Have an Ice & Rock Core?
If not, the standard theory for the formation of Jupiter & Saturn will
have to be rethought.
Main issues:
• Phase diagram of H2 and general understanding of interior
• Heavy-element abundances (C, N, O, S)
• Gravity field — nonspherical terms
• Free oscillations
(the wave of the future?)
References:
• Hubbard, W. B., Burrows, A., and Lunine, J. I. 2002, ARAA, 40,
103 “Theory of Giant Planets”
• Guillot, T. 1999, Planetary and Space Science 47, 1183 “A
Comparison of the Interiors of Jupiter and Saturn”
• Mosser, B., Maillard, J. P., and Mékarnia, D. 2000, Icarus, 144,
104 “New Attempt at Detecting the Jovian Oscillations”
A conventional 3-zone model of Jupiter’s interior:
(170 K, 1 bar)
H2
Radiative,
inhomogeneous?
(6500 K, 2 Mbar)
Ice & rock core?
(20,000 K, 40 Mbar)
Metallic H
Physical ingredients in a model: the usual equations
• Hydrostatic equilibrium
• Energy conservation; radiation transport by convection
• Mass conservation (geometry)
• Known (measured) abundances of the elements
• Equation of state P = P (ρ, T, µ)
“A principal feature that distinguishes giant planets and brown
dwarfs from stars is the nonideality of the thermodynamics of the
hydrogen-helium mixture in the interiors of the former.” (Hubbard et
al.)
Phase transition from “molecular” to “metallic” H poorly
understood, locus in (P, T ) diagram uncertain
• Pressure dissociation, then ionization
• Discontinuous (first-order) or continuous?
– If discontinuous, there must also be a discontinuity in He
abundance in thermal equilibrium
– If continuous, composition can also be continuous
• Transition barely reached in lab: diamond anvil cell, laser shock,
reverberation shock
Phase separation (immiscibility) of He and metallic H
• At T <
∼ 3000 K, homogeneous mixtures not allowed
• He droplets will separate out and sink
• Predictions are based on perturbation theory, which is known not
to work well for He
• Different theories disagree about whether phase separation will
occur under jovian conditions
=⇒
And here is a figure showing the effects of uncertainties in the
equation of state on the calculated P (ρ) in Jupiter
=⇒
Phase separation (immiscibility) of He and metallic H
• At T <
∼ 3000 K, homogeneous mixtures not allowed
• He droplets will separate out and sink
• Predictions are based on perturbation theory, which is known not
to work well for He
• Different theories disagree about whether phase separation will
occur under jovian conditions
=⇒
And here is a figure showing the effects of uncertainties in the
equation of state on the calculated P (ρ) in Jupiter
=⇒
Galileo entry probe mass spectrometer results on heavy-element
abundances relative to solar1
• Ne is 0.1 solar, believed dissolved in the He-rich phase
• Ar, Kr, Xe enhanced 3 × solar, enhanced by late-stage accretion
of icy planetesimals?
• C, S also about 3 × solar
• N not determined but known from attenuation of probe radio
signal to be 3 to 4 × solar in the deep atmosphere
• O not determined, water abundance too low
Implications for formation; alter input to interior models
1
Anders & Grevesse 1989
Gravity field as probe of interior
Planet rotationally distorted ⇒ potential is not spherical
Let s(θ) define an equipotential surface. (The parameter r is the
radius of a sphere with the same volume as the equipotential
surface.) Then the potential can be written


∞ Req
GM 
V (s, θ) = −
1− (
)2iJ2iP2i(cos θ)
s
n=1 s
where Req is the equatorial radius,
P2i(cos θ) are Legendre polymonials,
and the J2i are numbers called zonal gravitational moments.
The moments are given by
and so depend on the density distribution within the planet.
Measured values can therefore be diagnostic of the presence of a
central concentration.
Only the first three moments have been measured for Jupiter, in
contrast with dozens for the terrestrial planets.
With the enhanced heavy-element abundances implied by the Galileo
results, Guillot (1999) fitted models to the moments and found that
=⇒
the core mass is constrained between 0 and about 10 M⊕.
Seismology of Jupiter: a field in its infancy
The characteristic oscillation frequency is defined as the inverse of the
time needed for a sound wave to travel the diameter of the planet:
with sound speed c ≡ [(∂P/∂ρ)S ]1/2.
Because of the dependence of ν0 on the structural variables, it too is
diagnostic of the degree of central concentration. Measuring this
frequency would be a discriminant among the models.
An attempt to detect free oscillations
Mosser et al. used a Fourier transform spectrometer on the CFHT,
obtaining 6 hours of continuous observation on 6 consecutive nights.
Measured is the phase of a single interference fringe, determined
relative to the same fringe at the start of the recording of data.
The phase is given by
φ
v
= σ0 δ ,
2π
c
where σ0 is the mean wavenumber in the narrow spectral bandpass
observed, which was near a methane band at 1.1µm.
The field of view of the interferometer was 22 arcsec, less than half
the angular diameter of Jupiter at opposition. Therefore, guiding
errors may dominate the data. They were minimized by means of as
long an integration time as possible, about 3 s.
=⇒
Simulated power spectra in the frequency range 1 to 3.1 mHz show
that the observed power can be reproduced by jovian low-degree
pressure modes with rms amplitudes up to about 0.6 m s−1, which
could be excited by a momentum source such as turbulence.
Mode identification is not possible because of the poor sampling and
the contamination by guiding errors. All that can be done is to
search for regularity in the power spectrum. There should be a
splitting equal to the characteristic frequency, which will be smeared
out if there is a planetary ice-rock core.
A regularity in the spectrum is found with ∆ν = 142 ± 3µHz and is
identified as a measurement of the characteristic frequency.
The absence of noticeable smearing is interpreted as evidence that
the “core, if any, has a small size and/or a very low density contrast
with the fluid envelope.”
Typical models predict characteristic frequencies in the range 152 to
160 µHz. Therefore, if the observational value is correct, current
interior models will need to be modified. Inclusion of nonideal effects
of the hydrogen-helium mixture may be what is needed.
Conclusions
This problem is dominated by uncertainties in the basic physics.
Better laboratory studies of hydrogen at high pressure are urgently
needed.
However, more observations would also be useful:
• More detailed gravitational studies, by means of a low-periapse
polar Jupiter orbiter would give empirical values for higher-order
moments. They would be more sensitive to the planet’s interior
dynamics (differential rotation) than to its core mass, though.
• Better observational series, perhaps involving a global campaign,
might succeed in identifying planetary oscillation modes. This
could be a major test of interior models.
Hubbard et al. 2002
Guillot 1999
Equations of state:
disc. ph. trans ... continuous
Age of solar system