Skip to main content# Constraining the minimum core mass fraction and Fe/Mg ratio of close-in super-Mercury exoplanets

Presentation #222.02 in the session Exoplanets Formation & Evolution (Poster + Lightning Talk)

Published onOct 23, 2023

Constraining the minimum core mass fraction and Fe/Mg ratio of close-in super-Mercury exoplanets

Mercury’s core mass fraction (cmf) ≈ 70% is much higher than Earth’s 32% that is consistent with the Sun’s Fe/Mg ratio, implying Mercury formed differently (e.g., experienced a mantle-stripping impact). Super-Mercuries — exoplanets with cmf higher than consistent with their host stars’ Fe/Mg ratios — can likewise probe planet formation if their Fe/Mg ratios are constrained.

To avoid tidal disruption, planets with orbital periods *P* < 1 day must have mean densities > 7000 kg m^{-3} and cmf > 70% or so (Rappaport et al. 2013). More precise lower limits are found modeling self-compression in silicate mantle + Fe core planet and using the transit depth, which yields the equivalent planet radius, *R*_{T}. KOI 1843.03 has *P*=4.245 hr and *R*_{T} = 0.61 ^{+0.12}_{-0.08} *R*_{E} (Rappaport et al. 2013). Using a code they developed based on the algorithms of Hachisu (1986), Price and Rogers (2020) inferred KOI 1843.03 has cmf > 60% (for *R*_{T}=0.61*R*_{E}; 67% or 52% for *R*_{T}=0.53 *R*_{E} or *R*_{T}=0.73*R*_{E}).

We investigate KOI 1843.03 using the ‘kyushu’ code we wrote, also based on Hachisu (1986), benchmarked against Jacobi ellipsoids and Haumea (Dunham et al. 2019, Noviello et al. 2022). We model the stellar gravitational potential and rotation about the planet-star center of mass using a third-order tidal potential, which is easier to implement in the Hachisu algorithm, does not require calculating the small difference in two large terms, and largely avoids the need to parameterize orbital distance. For a bridgmanite mantle and ε Fe core, we find KOI 1843.03 has cmf > 58% (for *R*_{T}=0.61*R*_{E}; 61% or 52% for *R*_{T}=0.53 *R*_{E} or *R*_{T}=0.73*R*_{E}), reproducing the results of Price and Rogers (2020).

We include a mass fraction *f*_{S} of sulfur in the core, modeling it as a mixture of Fe and FeS and using the Voigt-Reuss-Hill average bulk modulus. For the case with *M*=0.52 *M*_{E} and *R*_{T} = 0.61 *R*_{E,} we find that for *f*_{S} = 0, 10, 20 or 30 wt%, minimum cmf increases: 58%, 64%, 75%, and 76%. The inferred Fe/Mg ratio varies as (1 - *f*_{S}) cmf / (1-cmf), increasing by up to 70% above the sulfur-free case. Also, the core of KOI 1843.03 is likely to have temperature > 5000 K, lowering the density by > 10%. We find this would raise minimum cmf from 58% to 68%, increasing the inferred Fe/Mg ratio by 50%.

Inclusion of light elements in the core, and thermal expansion effects, are needed to place tighter constraints on Fe/Mg ratios, but they are likely to be higher than has been estimated to date.