The disappearance of Jupiter's dilute core in favor of helium

1. Introduction.   Hydrogen (H), helium (He) and oxygen (O) are the most abundant elements in the Sun, as they were in the protosolar nebula. By analyzing the bulk composition of Jupiter, in which a large fraction of the nebula material is confined today, information on the conditions in the disk at the time of planet formation can be obtained. Here, we use the water abundance observed by Juno to infer Jupiter's heavy element mass fraction Z from interior modeling. 

The Galileo entry Probe measured a depletion in He, Ne, and water with respect to protosolar values [1]. While the He-Ne depletion is generally considered evidence of H/He phase separation and He-rain at Mbar pressures, the water abundance at depth where the atmosphere is supposed to be quiet and homogeneous remained obscure. Juno measurements of convective storms, lightning, the cloud height, the upper tropospheric CO abundance, as well as ongoing analysis of the microwave absorption, finally constrained the deep water abundance to be within 0.1x and 7x solar [2]. A 0.1x (1x/2x/3x) solar water (or O/H) abundance corresponds to Z of ~0.5x (1.2x/2x/2.8x) solar for Z_sol=0.015. The temperature at a reference level of 1-bar is observed to be T_1bar=166-174 K [3].

Jupiter interior models are in addition constrained by the gravitational harmonics J₂ and J₄. However, current models that fit the Juno gravity measurements struggle to reach 1x solar Z in the atmosphere. Higher values like 2x solar are out of reach. In practise, H/He adiabats tend to be too dense to permit adding heavy elements in the amount of 1x solar or more, where the J₂ and J₄ are most sensitive. Possibilities to reconcile the Jupiter models with the Juno measurements include substantial over-estimation of density along the Jupiter adiabat by current H/He-EOSs [4] or that Jupiter's adiabat is on a higher entropy, corresponding to T_1bar ~180 K, than seen in the atmosphere [5].  

Here, we insert an outer stable layer (OSL) with inverted He-gradient and investigate to what extent the low atmospheric-Z issue can be mitigated. Strong He-depletion at the bottom of the OSL is assumed to result from H/He phase separation at Mbar pressures. We validate this model against the (shifted) LHR0911 H/He phase diagram.

 

2. Method.   We place the OSL between 0.1 and 2 GPa. The temperature-gradient is adjusted to satisfy Ledoux-stability at R_ρ^-1=0.9. This places the OSL in the regime of fingering double diffusive convection [6].  We compute Jupiter models in sufficient agreement with the observed gravitational harmonics. We vary (i) the He-gradient dY across the OSL,  (ii) the transition pressure P_He between the He-depleted and He-rich layer at Mbar pressures, (iii) the deeper transition pressure P_Z between Z_atm and Z_deep, which are adjusted to fit J₂ and J₄, and (iv) T_1bar between 166 and 174 K. For H/He we use the CD21-EOS [7], while for Z we use water-Equations of State (EOS). 

 

3. Results for Z

Figure 1: Resulting Z_atm (open symbols) and Z_deep (filled) over the assumed He-gradient -dY across the Outer Stable Layer. The color scale shows P_He, and different symbols indicate T_1bar.

 

With the removal of He (larger -dY) and its deposition deeper down, Z_atm increases. A threshold of 1x atmospheric-Z can easily be reached and passed. For stronger He-depletion, up to 2x solar Z_atm is possible if He rain extends to deep levels of 3-4 Mbars, see Figure 1. Simultaneously, the dilute core, which is clearly seen at dY=0, becomes more dilute (Z_deep decreases). Eventually, Z_atm ~ Z_deep: a homogeneous-Z interior has emerged with a Z of 1.5-2x solar and a few M_E rock core mass. The dilute core has disappeared.

 

4. Comparison to H/He phase diagram.   We compare the deep He-depletion at Mbar levels of our Jupiter models with the He-depletion predicted by the (shifted) LHR0911 H/He-phase diagram [8]. For adiabatic standard models (dY=0) based on CD21-EOS, a fine-tuned shift of this H/He phase diagram by -1100 K is needed to yield the observed atmospheric value Y_Gal ~ 0.238. For our models with variable dY, consistency occurs where the region spanned by the points (Jupiter models) and the lines (H/He phase diagram) overlap. The overlap region is wide and relaxes the required shift to be within 1000-1200 K, see Figure 2.

Figure 2: Lines: He depletion along adiabats defined by T_1bar (color code along the lines) according to the LHR0911 H/He-phase diagram [8] for different shifts thereof. Points: He depletion at the 1 Mbar level of P-T profiles with OSL.

 

5. Conclusions.  Insertion of an Outer Stable Layer with inverted He-gradient lifts Z_atm up to 2x solar (O/H = 2x solar). Such Jupiter models have a homogeneous-Z interior and a small compact core. The dilute core has disappeared in favor of an enhanced He abundance. We furthermore find that a H/He phase diagram than can explain the observed atmospheric He-abundance will as well be consistent with strong depletion at Mbar depths, in which case the deep adiabats are cold. This may point to an actually super-adiabatic, stable He-rain region. Indeed, an extended deep stable region is suggested by Jupiter's gravitational response to tides observed by Juno [9]. 

 

6. References.   [1] Atreya, Mahaffy, Niemann et al Pl.Sp.Sci 51:105 (2003)   [2] Cavalie, Lunine, Mousis SSRv. 220:8 (2024)  [3] Gupta, Atreya, Steffes, et al PSJ 3:159 (2022)  [4] Howard, Guillot, Bazot et al AA 672:A33 (2023)  [5] Miguel, Bazot, Guillot et al AA 662:A18 (2022)   [6] Brown, Garaud, Stellmach ApJ 768:34 (2014)  [7] Chabrier & Debras ApJ 917:4 (2021)   [8] Lorenzen, Holst, Redmer PRB 84:235109 (2011)  [9] Idini & Stevenson 3:89 PSJ (2022)