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

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 an updated H–He equation of state and atmospheric boundary conditions that vary with envelope metallicity, we quantify the bulk heavy element content of 147 warm (&lt;1000 K) giant planets with well-measured masses and radii, more than tripling the sample size studied in D. P. Thorngren et al. These measurements reveal that the population’s heavy element mass follows the relation <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>Z</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>core</mml:mi> </mml:msub> <mml:mo>+</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>Z</mml:mi> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>M</mml:mi> <mml:mi>core</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> , with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">core</mml:mi> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>14</mml:mn> <mml:mo>.</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.6</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>1.8</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> M ⊕ , f Z = 0.09 ± 0.01, and an astrophysical scatter of 0.66 ± 0.08 × M Z . The classical core-accretion scenario ( Z p = 1 at 10 M ⊕ and Z p = 0.5 at 20 M ⊕ ) is inconsistent with the population. At low planet masses (≪150 M ⊕ ), <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">Z</mml:mi> </mml:mrow> </mml:msub> <mml:mo>∼</mml:mo> <mml:msub> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="normal">core</mml:mi> </mml:mrow> </mml:msub> </mml:math> and as a result, Z p = M Z / M p declines linearly with M p . However, bulk metallicity does not continue to decline with planet mass and instead flattens out at f Z ∼ 0.09 (∼7 × solar metallicity). When normalized by stellar metallicity, Z p / Z ⋆ flattens out at 3.3 ± 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.