Revising the Giant Planet Mass-Metallicity Relation: Deciphering the Formation Sequence of Giant Planets

TL;DR

This study refines our understanding of giant planet formation by expanding the bulk metallicity census to $147$ warm giants and updating interior and atmospheric physics with a modern H–He EOS and envelope metallicity dependent boundaries. The authors deduce a robust mass–metallicity relation described by $M_Z = M_{\rm core} + f_Z (M_p - M_{\rm core})$, finding $M_{\rm core} = 14.7^{+1.8}_{-1.6}\,M_\oplus$ and $f_Z = 0.09 \pm 0.01$, with significant astrophysical scatter $\sigma_{\rm mult} \approx 0.66\,M_Z$. The results contradict the classical core–accretion expectation of a simple $Z_p \sim 1$ at low masses and $Z_p \sim 0.5$ at $20\,M_\oplus$, instead showing a flattening metallicity at high masses and a persistent enrichment during gas accretion, yielding bulk metallicities near several times solar. These findings support a formation picture in which giant planets continue to accrete metal-rich material during their growth, place important constraints on runaway accretion timing, and provide a benchmark for interpreting distant giant planets and atmospheric metallicities in the context of planet formation pathways.

Abstract

The rate at which giant planets accumulate solids and gas is a critical component of planet formation models, yet it is extremely challenging to predict from first principles. Characterizing the heavy element (everything other than hydrogen and helium) content of giant planets provides important clues about their provenance. Using thermal evolution models with updated H-He EOS and atmospheric boundary condition that varies with envelope metallicity, we quantify the bulk heavy element content of 147 warm ($< 1000$ K) giant planets with well-measured masses and radii, more than tripling the sample size studied in Thorngren et al. 2016. These measurements reveal that the population's heavy element mass follows the relation $M_{\rm Z} = M_{\rm core} + f_Z (M_{\rm p} - M_{\rm core})$, with $M_{\rm core} = 14.7^{+1.8}_{-1.6}$ Earth masses (M$_\oplus$), $f_Z = 0.09 \pm 0.01$, and an astrophysical scatter of $0.66 \pm 0.08 \times M_Z$. The classical core-accretion scenario ($Z_{\rm p} = 1$ at 10 M$_\oplus$ and $Z_{\rm p} = 0.5$ at 20 M$_\oplus$) is inconsistent with the population. At low planet masses ($<< 150$ M$_\oplus$), $M_{\rm Z} \sim M_{\rm core}$ and as a result, $Z_{\rm p} = M_{\rm Z} / M_{\rm p}$ declines linearly with $M_{\rm p}$. However, bulk metallicity does not continue to decline with planet mass and instead flattens out at $f_Z \sim 0.09$ ($\sim 7 \times$ solar metallicity). When normalized by stellar metallicity, $Z_{\rm p} / Z_\star$ flattens out at $3.3 \pm 0.5$ at high planet masses. This explicitly shows that giant planets continue to accrete material enriched in heavy elements during the gas accretion phase.

Figures (14)

• Figure 1: The radii and masses of the planets in our sample. The dotted and dashed lines show the mass-radius relation for pure H-He planets at 0.5 and 5 Gyr for an incident flux of $10^8$ erg s$^{-1}$ cm$^{-2}$.
• Figure 2: Median estimates of the bulk metallicity for our planet sample assuming the metals are distributed uniformly throughout the planet (y-axis) and our fiducial choice (x-axis, $M_{\rm Z} \leq 10 \, M_\oplus$ in the core, rest of the metals in the envelope).
• Figure 3: Evolution models for a 0.3 M$_{\rm Jup}$ planet for different bulk metallicities assuming the metals are uniformly distributed inside the planet (i.e., no central core). The solid lines correspond to our updated evolution model. The models corresponding to the dashed lines are indicated in the panel titles. In the top left panel, we compare with models that use a solar metallicity atmosphere but the same EOS for H-He and metals as our model. In the top right panel, we compare with models that use our adopted metal EOS and atmosphere models but with the SCvH EOS for H-He. In the bottom left panel, we compare with models that use ANEOS for metals. In the bottom right panel, we compare our evolution models with those calculated as in Thorngren2016.
• Figure 4: Evolution models for a 3 M$_{\rm Jup}$ planet for different bulk metallicities assuming the metals are uniformly distributed inside the planet. The solid lines correspond to our updated evolution model. The models corresponding to the dashed lines are indicated in the panel titles. See Figure \ref{['fig:saturn_evol_comparison']} caption for more details.
• Figure 5: The probability distribution of the calculated metal mass for a sample of three planets. For HAT-P-18 b, the distribution provides an upper limit on its metal mass. TOI-1439 b's distribution is truncated at its total planet mass while WASP-139 b's metal distribution is nearly Gaussian. For planets such as HAT-P-18 b and TOI-1439 b, we fit a truncated normal distribution to the metal distribution and use it to calculate the model likelihood.