A Falsifiable Hypothesis for the Formation and Long-Term Preservation of Jupiter’s Extended Heavy-Element Gradient
Abstract
Measurements of Jupiter’s gravitational field by NASA’s Juno spacecraft have challenged the traditional picture of Jupiter as a nearly homogeneous hydrogen-helium envelope surrounding a sharply bounded compact core. Interior models compatible with Juno commonly favor an extended region enriched in heavy elements—a “dilute” or “fuzzy” core—although its precise mass and radial extent remain dependent on the adopted equation of state and interior assumptions.
The origin of this structure remains unresolved. Conventional core-accretion calculations naturally generate primordial composition gradients because incoming solids dissolve, vaporize, or settle within the growing envelope, but these gradients can be substantially more compact than some present-day Jupiter structures require. A giant impact was proposed as an alternative means of dispersing a compact core, but recent high-resolution impact and long-term evolution simulations find that plausible impacts do not robustly produce the required surviving fuzzy core. Meanwhile, self-consistent evolutionary calculations published in 2026 indicate that double-diffusive convection redistributes less than approximately one Earth mass of heavy material over 4.56 Gyr under the modeled conditions, implying that much of Jupiter’s extended composition structure may need to be established during formation.
This paper proposes a distinct formation-stage mechanism: Accretion-Driven Wave Entrainment (ADWE). During runaway gas accretion, gravitational energy released by high-velocity, multidimensional inflow is processed through accretion shocks and circumplanetary flows. The hypothesis proposes that a finite fraction of this energy is transmitted into proto-Jupiter as pressure fluctuations, acoustic waves, internal motions, and shear. When these disturbances encounter the pre-existing, molecular-weight-stratified heavy-element region, their dissipation produces transient turbulent entrainment that transports heavy material outward and broadens the primordial composition gradient.
When runaway accretion terminates, the external mechanical-energy source collapses. The remaining positive molecular-weight gradient then suppresses large-scale overturning, while comparatively weak post-formation compositional transport allows the broadened structure to survive for billions of years.
ADWE is falsifiable at several independent stages. It fails if realistic multidimensional accretion simulations cannot deliver sufficient mechanical energy to the deep composition-gradient region; if that energy cannot produce measurable outward heavy-element transport; if all sufficiently energetic cases homogenize the planet rather than producing a finite gradient; or if the resulting composition profile cannot survive 4.56 Gyr and reproduce Jupiter’s present gravitational constraints.
1. Scientific Problem
Juno’s gravitational measurements strongly constrain Jupiter’s internal density distribution. Models constructed from those data commonly favor deep enrichment in heavy elements and can include a dilute core extending through a significant portion of Jupiter rather than a simple compact core-envelope boundary. The exact compositional solution is not unique because gravity measures density rather than chemical composition directly.
Standard formation theory already offers part of the explanation.
Detailed core-accretion calculations show that incoming planetesimals need not remain intact until reaching Jupiter’s center. As proto-Jupiter grows hotter and more massive, solids can dissolve or vaporize in the envelope, naturally producing an inwardly increasing heavy-element abundance rather than a perfectly sharp core boundary.
The difficulty is producing the appropriate extent of the enriched region while simultaneously preserving it.
Müller, Helled, and Cumming found that the standard formation and evolutionary histories they investigated did not produce the extended fuzzy-core structures required by the interior models they tested. Recent impact calculations have also weakened the giant-impact alternative, concluding that Jupiter’s fuzzy core is more likely associated with the formation process itself.
At the other end of Jupiter’s history, recent calculations suggest that post-formation double-diffusive transport may be too weak to substantially broaden an initially compact composition gradient.
The unresolved physical gap can therefore be stated narrowly:
What process operating during Jupiter’s formation could have broadened a pre-existing heavy-element gradient substantially, without completely homogenizing the planet, and then naturally switched off so that the resulting structure could survive for billions of years?
ADWE is proposed as one answer to that question.
2. Hypothesis Statement
Accretion-Driven Wave Entrainment Hypothesis
Jupiter initially acquired an inwardly increasing heavy-element gradient through conventional solid accretion, dissolution, vaporization, and settling.
During early runaway gas accretion, the rapidly increasing gravitational power of incoming gas generated multidimensional accretion shocks, pressure disturbances, waves, shear, and turbulent motions. Giant-planet formation calculations independently show that late gas accretion is intrinsically multidimensional and involves complex flows associated with the planet and circumplanetary environment rather than ideal spherical deposition.
ADWE proposes that part of this mechanical disturbance propagated below the accretion region and interacted with Jupiter’s existing molecular-weight gradient.
The central causal chain is Runaway Gas Accretion→Mechanical Energy Injection→Deep Wave/Shear Transport→Heavy-Element Entrainment→Broadened Gradient
followed by Accretion Shutoff→Mechanical Forcing Collapse→Compositional Stabilization→Long-Term Preservation
The present dilute core is therefore hypothesized to be a fossil structure produced during a temporary mechanically forced mixing interval.
3. THD Structural Interpretation
Triune Harmonic Dynamics is used here as an organizational framework for the physical transition. It does not replace hydrodynamics, thermodynamics, planetary evolution, or transport theory.
| THD Phase | Jupiter Formation State |
|---|---|
| Base Phase | Ordinary formation processes establish an initially concentrated heavy-element gradient. |
| Pressure Phase | Runaway gas accretion greatly increases mechanical-energy input, wave excitation, shear, and transient mixing. |
| Integration Phase | Heavy elements become distributed through a broader region; accretion weakens, mechanical mixing terminates, and the remaining composition gradient stabilizes. |
In compact form, Primordial Gradient→Transient Forced Redistribution→Fossil Dilute Core.
The physical hypothesis stands independently of the THD terminology and can therefore be tested entirely with conventional planetary physics.
4. System Definition
The modeled system begins immediately before or near the onset of runaway gas accretion and extends through Jupiter’s present age.
The simulation must include four successive regimes:
- formation of an initial heavy-element gradient;
- runaway gas accretion;
- termination of rapid accretion;
- thermal and compositional evolution for approximately 4.56 Gyr.
The fundamental state variables include Mp(t),Rp(t),M˙g(t), ρ(r,t),T(r,t),P(r,t), Z(r,t),μ(r,t),
and the velocity field u(r,θ,ϕ,t).
Here:
- Mp is planetary mass,
- Rp is planetary radius,
- M˙g is gas-accretion rate,
- Z is heavy-element mass fraction,
- μ is mean molecular weight,
- u is fluid velocity.
The principal output is not merely the final core radius.
It is the complete evolution Z(r,t).
5. Accretion Energy Source
The approximate gravitational power released by gas accretion is Lacc=RpGMpM˙g(1)
where G is the gravitational constant.
Equation (1) represents an available energy scale, not an assumption that all accretion energy enters Jupiter’s deep interior.
Define ϵmech
as the fraction converted into mechanically propagating disturbances rather than immediately radiated or thermalized locally.
Then Lmech=ϵmechLacc(2)
with 0≤ϵmech≤1.
A second quantity is required because even mechanically generated energy need not reach the deep composition gradient.
Let Tg(r,t)
be the transmission fraction from the accretion region to the heavy-element gradient.
The mechanical power reaching that region is therefore Ldeep=TgϵmechRpGMpM˙g(3)
with 0≤Tg≤1.
Neither ϵmech nor Tg should be chosen merely to make the hypothesis work.
They are outputs to be measured from multidimensional radiation-hydrodynamic simulations.
6. Mechanical Transmission Observable
A key advantage of the hypothesis is that the proposed transmission pathway can be directly measured in a simulation.
For pressure-driven disturbances, a first-order radial wave-energy flux can be estimated from correlated pressure and velocity perturbations: Fwave=⟨p′ur′⟩(4)
where
- p′ is the pressure fluctuation,
- ur′ is the fluctuating radial velocity,
- angle brackets represent an appropriate temporal and angular average.
The corresponding luminosity is Lwave(r)=4πr2Fwave(r)(5)
for the spherically averaged component.
Additional Reynolds-stress and kinetic-energy transport terms should be included in the complete numerical energy budget.
The critical observational quantity in the simulation is therefore Ldeep(r,t),
not simply the accretion shock luminosity.
7. Composition-Gradient Stability
The primordial gradient is stabilized by an inward increase in mean molecular weight.
For a compressible planetary fluid, the Brunt–Väisälä frequency can be written schematically as N2=HPg[∇ad−∇+δϕ∇μ](6)
where ∇=dlnPdlnT, ∇μ=dlnPdlnμ, δ=−(∂lnT∂lnρ)P,μ,
and ϕ=(∂lnμ∂lnρ)P,T.
The compositional contribution is Nμ2=HPgδϕ∇μ(7)
with the convention Nμ2>0
for stabilizing molecular-weight stratification.
Previous evolutionary calculations have demonstrated that sufficiently strong primordial composition gradients can preserve non-adiabatic deep regions for very long periods, although the amount of mixing depends strongly on the assumed initial thermal structure and transport prescription.
8. Proposed Entrainment Mechanism
ADWE does not require the entire composition gradient to become convectively unstable.
Instead, waves and accretion-generated shear can intermittently produce local turbulent entrainment.
A useful diagnostic is the compositional Richardson number Riμ=S2Nμ2(8)
where S is the relevant local shear rate.
Large Riμ indicates strong stabilization relative to shear, while lower values indicate conditions more favorable to shear-driven mixing.
No universal critical value is assumed here because proto-Jupiter is rotating, compressible, strongly stratified, and potentially wave driven.
The threshold must emerge from the hydrodynamic calculation.
9. Heavy-Element Transport Equation
The heavy-element abundance obeys ∂t∂Z+u⋅∇Z=∇⋅(Deff∇Z)+SZ(9)
where SZ represents continuing deposition or removal of heavy material.
The effective diffusivity can be decomposed as Deff=Dmicro+Dconv+DDD+DADWE(10)
where
- Dmicro is microscopic diffusion,
- Dconv represents ordinary convective mixing,
- DDD represents double-diffusive transport,
- DADWE is the additional transient transport produced by accretion-driven mechanical forcing.
Crucially, DADWE should be measured rather than prescribed.
For a radial mean composition profile, DADWE=−∂Z/∂r⟨ur′Z′⟩(11)
where defined.
If heavy-element abundance decreases outward, ∂r∂Z<0,
then positive outward compositional transport corresponds to ⟨ur′Z′⟩>0
and therefore DADWE>0.
This provides an explicit measurable bridge between the proposed mechanism and the composition evolution.
10. Energetic Condition for Core Broadening
The approximate power required for mixing against stable compositional buoyancy can be represented by Lbuoy=∫VgρNμ2DADWEdV(12)
where Vg is the volume containing the relevant composition gradient.
This expression has dimensions of power and provides a useful energetic diagnostic for turbulent compositional transport.
Define the Accretion Mixing Number ΠA=LbuoyLdeep(13)
for a specified redistribution rate.
Thus, ΠA<1
means the proposed transport rate requires more buoyancy work than the available deep mechanical power can provide.
Conversely, ΠA≳1
is a necessary energetic condition for that transport rate, although it is not by itself sufficient to prove that the hydrodynamics actually produces the mixing.
11. Integrated Formation-Energy Test
The total mechanical energy reaching the deep composition gradient during the relevant accretion interval is Edeep=∫t1t2Tg(t)ϵmech(t)Rp(t)GMp(t)M˙g(t)dt(14)
Let ΔEZ
be the minimum self-consistently calculated increase in gravitational and internal potential energy required to transform the initial heavy-element profile Zi(r) into the broadened profile Zf(r).
A necessary condition for ADWE is Edeep≥ΔEZ(15)
within the physically permitted simulation family.
Define B=ΔEZEdeep(16)
as the integrated broadening parameter.
The hypothesis predicts three qualitative regimes: B≪1⇒negligible broadening, B∼1⇒significant but finite redistribution,
while sufficiently large effective coupling could yield B≫1⇒excessive mixing or homogenization.
A Jupiter-like solution therefore requires an intermediate physical regime.
That is itself falsifiable.
12. Self-Termination Prediction
A defining feature of ADWE is that the dominant mixing source is temporary.
Because Lacc∝M˙g,
the termination of runaway accretion requires M˙g→0
and therefore Ldeep→0.
The hypothesis consequently predicts M˙g→0⇒DADWE→0(17)
apart from residual free oscillations or decaying turbulence.
The planet is then left with a broadened molecular-weight gradient but without the external mechanical forcing that created it.
This is the proposed freeze-out mechanism.
13. Long-Term Preservation
After formation, Deff=Dmicro+Dconv+DDD,
because DADWE≃0.
The characteristic compositional-mixing timescale across a surviving gradient of characteristic scale ℓZ is τZ∼DpostℓZ2(18)
where Dpost represents the effective post-formation compositional diffusivity.
A substantial portion of the ADWE-generated gradient must satisfy approximately τZ≳4.56 Gyr(19)
or otherwise survive explicitly in a time-dependent evolutionary calculation.
Recent work strengthens the plausibility of preservation rather than late broadening: self-consistent double-diffusive models found less than roughly 1M⊕ of heavy-element redistribution in Jupiter and Saturn over their modeled 4.56-Gyr evolution.
14. Specific Predictions
ADWE makes several linked predictions.
Prediction 1 — Mechanical energy penetrates beneath the accretion shock
Multidimensional simulations must show Fmech(r,t)=0
at the primordial heavy-element boundary during runaway accretion.
Prediction 2 — Mixing is temporally correlated with runaway accretion
The rate of heavy-element redistribution should increase during high-M˙g intervals.
In particular, DADWE
should statistically track the deep mechanical-energy flux rather than simply elapsed planetary age.
Prediction 3 — Heavy material moves outward
For some portion of the initial gradient, FZADWE=ρ⟨ur′Z′⟩>0(20)
under the convention that positive radial direction is outward.
Prediction 4 — Mixing is spatially concentrated
Enhanced dissipation and compositional transport should occur preferentially where mechanically transmitted waves and shear interact with the composition-gradient region.
Prediction 5 — The planet is not completely homogenized
Successful simulations must retain drdZ<0
through a finite deep region after runaway accretion.
Prediction 6 — Broadening largely precedes long-term cooling
The majority of the required extension should be generated during the formation-stage mechanical-forcing interval, not gradually over the next several billion years.
Prediction 7 — The resulting structure survives
After evolution to Jupiter’s current age, a substantial heavy-element gradient must remain.
Prediction 8 — The evolved density distribution matches Jupiter
The final model must reproduce Juno-compatible gravitational moments after consistently accounting for rotational and wind contributions.
For example, define χJ2=n∑[σJnJnmodel−Jnobs]2(21)
for the selected gravitational moments.
The comparison must account for uncertainties in the equation of state and dynamic contributions rather than treating the measured Jn as purely hydrostatic quantities.
15. Experimental and Computational Test Protocol
The hypothesis can be tested without waiting for a new spacecraft mission.
Stage A — Establish the initial condition
Use conventional planet-formation calculations to generate a proto-Jupiter heavy-element profile Zi(r)
before or near runaway gas accretion.
The initial dilute core must not be artificially chosen to resemble present Jupiter.
That would make the test circular.
Stage B — Simulate runaway accretion
Perform multidimensional radiation-hydrodynamic calculations resolving:
- planetary accretion flow,
- circumplanetary flow,
- accretion shocks,
- pressure fluctuations,
- rotation,
- the deep envelope,
- the primordial composition-gradient region.
Existing calculations already demonstrate that multidimensional giant-planet accretion can be geometrically complex and that much of the gas entering the Hill sphere does not simply fall radially onto the planet.
Stage C — Measure energy transmission
Measure Fwave,Fkin,FReynolds,
and therefore the mechanical luminosity reaching the composition-gradient region.
Do not infer deep coupling merely from the large value of Lacc.
Stage D — Measure composition transport
Introduce an active heavy-element distribution and calculate ⟨ur′Z′⟩, DADWE(r,t),
and the time evolution of Z(r,t).
Stage E — Terminate accretion
Reduce the external gas supply according to a physically plausible disk-dispersal or gap-limited accretion history.
The simulation should determine whether DADWE
declines naturally.
Stage F — Long-term evolution
Pass the resulting post-formation structure into a planetary evolution calculation incorporating physically justified:
- convection,
- thermal diffusion,
- compositional diffusion,
- double-diffusive transport,
- helium phase separation where appropriate,
- equation-of-state physics.
Evolve the model to t=4.56 Gyr.
Stage G — Blind present-day comparison
Only after the formation-to-evolution simulation is complete should the final structure be tested against present-day Jovian constraints.
The strongest version would withhold at least one observational constraint from parameter calibration and use it for out-of-sample validation.
16. Confirmation Markers
The hypothesis receives strong support only if the following chain is recovered.
C1. Realistic runaway gas accretion produces measurable mechanical-energy transport below the accretion region.
C2. A non-negligible fraction reaches the primordial composition-gradient region.
C3. Wave breaking, shear, or associated turbulence produces measurable outward heavy-element flux.
C4. DADWE>0
becomes dynamically important during the runaway phase.
C5. The heavy-element gradient broadens substantially compared with an otherwise identical control simulation without the accretion-driven mechanical transport.
C6. The process does not completely homogenize Jupiter.
C7. The additional transport diminishes naturally as M˙g
declines.
C8. A broad positive molecular-weight gradient survives long-term evolution.
C9. The evolved Jupiter is simultaneously compatible with present mass, radius, thermal evolution, and Juno gravity constraints.
C10. Most importantly, the successful dilute core emerges without inserting a present-day dilute-core profile as an initial condition.
That final criterion distinguishes prediction from curve fitting.
17. Falsification Conditions
ADWE is deliberately constructed so that several independent results can reject it.
F1 — Deep mechanical coupling is energetically inadequate
If realistic simulations establish Edeep<ΔEZ
for all physically credible Jupiter accretion histories, ADWE is falsified.
F2 — Accretion disturbances remain shallow
If shocks and associated fluctuations are efficiently radiated or thermalized near the planetary surface and Fmech≈0
at the composition-gradient region, the proposed mechanism is falsified.
F3 — No significant outward compositional flux occurs
If ⟨ur′Z′⟩≈0
through the relevant region despite realistic runaway accretion, the entrainment component fails.
F4 — Insufficient broadening
If the resulting change Zi(r)→Zf(r)
is much smaller than required by all physically admissible Juno-compatible interior models, the mechanism fails as an explanation of Jupiter’s dilute core.
F5 — Energetic cases always homogenize the interior
If every simulation capable of substantially moving heavy elements also eliminates the stabilizing gradient, drdZ→0,
then there is no physically accessible ADWE regime and the hypothesis is falsified.
F6 — Required efficiency is unphysical
If agreement requires ϵmech>1
or Tg>1,
the hypothesis is immediately impossible.
It should also be rejected if the required efficiencies fall within mathematically allowed values but are decisively excluded by independent hydrodynamic simulations.
F7 — Broadening does not correlate with accretion
If the heavy-element redistribution occurs independently of M˙g
or continues essentially unchanged after accretion forcing disappears, the specific ADWE causal interpretation fails.
F8 — The generated gradient cannot survive
If every ADWE-generated profile is destroyed on a timescale τZ≪4.56 Gyr
under physically realistic evolutionary calculations, the preservation component is falsified.
F9 — Present Jupiter is incompatible with the outcome
If no ADWE-generated, long-term-evolved composition profile can reproduce Jupiter’s present structural and gravitational constraints within propagated uncertainties, the full hypothesis is falsified.
18. Novelty Assessment
The novelty claim must be narrow.
The following ideas are not novel:
- Jupiter probably contains an extended heavy-element gradient;
- primordial composition gradients arise naturally during formation;
- solids can dissolve or vaporize within proto-Jupiter;
- convection can erode gradients;
- stable molecular-weight gradients can inhibit mixing;
- double-diffusive transport can operate;
- giant impacts have been proposed to create a dilute core;
- runaway giant-planet accretion involves shocks and multidimensional flows.
Those elements already appear extensively in the literature.
The narrower proposed contribution is:
The mechanical energy of runaway gas accretion itself acts as a temporary deep compositional-transport source: accretion-driven pressure waves, shear, and associated turbulence entrain already-deposited heavy material outward, broadening the primordial core before the forcing disappears.
In the literature reviewed through August 2026, I did not identify a study that closes the entire causal chain multidimensional runaway accretion→Fmech,deep→⟨ur′Z′⟩→Zf(r)→4.56 Gyr evolution→Jn
as a proposed explanation for Jupiter’s dilute core. Existing work instead treats formation-generated deposition profiles, subsequent thermal/compositional evolution, giant impacts, or double-diffusive/core-erosion processes. That conclusion is a literature-search result rather than proof that no related suggestion exists anywhere, so a formal pre-submission bibliographic review would still be necessary before asserting priority.
This distinction matters. The proposed novelty is not “runaway accretion affects Jupiter.”
It is specifically: Accretion mechanical energy→deep transient compositional entrainment
as the missing broadening mechanism.
19. Relationship to Current Jupiter Research
Recent results arguably make this hypothesis more testable.
Meier et al. found that a giant impact is unlikely to be responsible for Jupiter’s fuzzy core and concluded that the structure is likely connected to formation.
Fuentes et al. subsequently found that self-consistent double-diffusive transport is weak in their Jupiter and Saturn evolutionary calculations, leaving primordial gradients largely intact over 4.56 Gyr.
Meanwhile, recent primordial-structure reconstructions favor a metal-rich dilute region inherited from formation and place constraints on Jupiter’s early entropy, radius, accretion history, and shock energetics.
Taken together, these findings increasingly shift the core question toward the formation epoch: How was the broad initial gradient actually produced?
ADWE directly targets that missing step.
20. Scientific Implications if Confirmed
If validated, Jupiter’s dilute core would become more than a record of what materials Jupiter accreted.
It would become a record of how Jupiter accreted them.
The present composition profile could preserve information about: M˙g(t),
the geometry of circumplanetary accretion, ϵmech,
wave transmission,
rotation,
and primordial stratification.
Two planets with similar total heavy-element masses could consequently possess different internal architectures because they experienced different mechanical accretion histories.
This produces a testable comparative prediction.
If ADWE is a general giant-planet process, the degree of core dilution should correlate statistically with formation parameters that determine accretion power and deep mechanical coupling—not merely with total planetary metallicity.
Saturn would provide the most obvious Solar System comparison, although Jupiter and Saturn need not occupy the same regime.
Young giant exoplanets could eventually provide a broader population test.
21. Limitations
Several limitations should be explicit.
First, Jupiter’s present heavy-element distribution is not uniquely determined by Juno. Gravity tightly constrains density, but composition inference remains dependent on hydrogen-helium equations of state, temperature structure, helium distribution, rotation, and model architecture.
Second, the proposed transmission efficiency Tg
is presently unknown. Its uncertainty is not a license to choose a convenient value. Determining it is one of the main tests of the hypothesis.
Third, the simple wave-flux equation in Eq. (4) does not capture every form of mechanical transport. A complete simulation must include the full compressible energy and Reynolds-stress budgets.
Fourth, Eq. (12) is an energetic diagnostic rather than a substitute for explicit hydrodynamics.
Fifth, rotation may substantially alter wave propagation, shear stability, turbulence, and compositional entrainment.
Sixth, the physical form and composition of Jupiter’s heavy elements remain uncertain.
Seventh, ADWE requires a pre-existing composition gradient. It is not proposed as the origin of Jupiter’s heavy elements.
Finally, demonstrating that Jupiter possessed enough total accretion energy does not validate the hypothesis.
The required experimental bridge is: Lacc→Fmech,deep→FZ→Z(r,t)→survival→Jn
Every arrow must be quantitatively demonstrated.
22. Final Hypothesis Test Statement
The energetic requirement is Edeep≥ΔEZ
during a finite runaway-accretion interval.
The transport requirement is FZADWE=ρ⟨ur′Z′⟩>0
through a significant portion of the primordial heavy-element gradient.
The shutdown requirement is M˙g→0⇒DADWE→0
and the preservation requirement is approximately τZ≳4.56 Gyr
for enough of the resulting structure to remain compatible with Jupiter today.
Therefore: Runaway Accretion⇓Deep Mechanical Energy⇓Transient Heavy-Element Entrainment⇓Extended Composition Gradient⇓Accretion Shutoff + Ledoux Stability⇓Present-Day Dilute Core
Final One-Sentence Hypothesis
Jupiter’s extended dilute core formed when pressure waves, shear, and turbulence generated during runaway gas accretion transmitted sufficient mechanical energy into a narrower primordial heavy-element gradient to entrain material outward without fully homogenizing the planet; when rapid accretion ended, this additional mechanical transport disappeared and the surviving molecular-weight gradient preserved the broadened structure for billions of years—a hypothesis falsified if realistic formation simulations cannot demonstrate the required deep energy transmission, outward compositional flux, finite core broadening, long-term survival, and compatibility with Juno’s gravitational constraints.
Selected References
Wahl et al. (2017), Comparing Jupiter interior structure models to Juno gravity measurements and the role of a dilute core.
Lozovsky et al. (2017), Jupiter’s formation and its primordial internal structure.
Vazan, Helled & Guillot (2018), Jupiter’s evolution with primordial composition gradients.
Müller, Helled & Cumming (2020), The Challenge of Forming a Fuzzy Core in Jupiter.
Helled & Stevenson (2024), The Fuzzy Cores of Jupiter and Saturn.
Militzer & Hubbard (2024), Study of Jupiter’s Interior: Comparison of 2, 3, 4, 5, and 6 Layer Models.
Meier et al. (2025), On the origin of Jupiter’s fuzzy core: constraints from N-body, impact and evolution simulations.
Knierim et al. (2025), Further constraints on Jupiter’s primordial structure.
Fuentes et al. (2026), Self-Consistent Evolution Models Show Weak Double-Diffusive Mixing in Jupiter and Saturn.
This version fixes the equation problem and also strengthens the paper relative to the previous draft: the novel mechanism now has an explicit source equation, transmission variable, measurable wave flux, measurable heavy-element flux, energy budget, shutdown equation, preservation condition, and end-to-end falsification pathway