Evidence of 1:1 slope between rocky Super-Earths and their host stars

TL;DR

This study tests whether rocky exoplanets share a primordial, 1:1 iron-mass-fraction relationship with their host stars by building a self-consistent dataset of 21 planets around 20 stars and applying a sophisticated interior-structure model alongside a stellar-to-planet chemical translation. Using Bayesian linear regression with a skewed-Gaussian likelihood and weighting boundary cases by rocky probability, the authors find a near 1:1 relation in Fe-MF space: $m = 0.94^{+1.02}_{-1.07}$ and $c = -0.02^{+0.31}_{-0.29}$, though substantial uncertainties remain and no strong subpopulations are detected. The planets exhibit a wider range of refractory compositions than their stars, suggesting real formation diversity or measurement scatter; mock-population tests indicate that ~15% of similar samples could produce the observed slope by chance, and a much larger sample (≈150 planets) is needed to decisively test a primordial origin. The work reconciles some prior conflicting results by emphasizing consistent stellar data treatment and boundary handling, and it highlights PLATO-era prospects for obtaining the requisite statistical power to constrain planet formation scenarios and galactic chemical evolution effects.

Abstract

The relationship between the composition of rocky exoplanets and their host stars is fundamental to understanding planetary formation and evolution. However, previous studies have been limited by inconsistent datasets, observational biases and methodological differences. This study investigates the compositional relationship between rocky exoplanets and their host stars, utilizing a self-consistent and homogeneous dataset of 21 exoplanets and their 20 host stars. By applying sophisticated interior structure modeling and comprehensive chemical analysis, we identify a potential 1:1 best-fit line between the iron-mass fraction of planets and their host stars equivalent with a slope of $m = 0.94^{+1.02}_{-1.07}$ and intercept of $c = -0.02^{+0.31}_{-0.29}$. This results are consistent at the 1$σ$ level with other homogeneous studies, but not with heterogeneous samples that suggest much steeper best-fit lines. Although, our results remain tentative due to sample size and data uncertainties, the updated dataset significantly reduces the number of super-Mercuries from four to one, but it remains that several high-density planets are beyond what a primordial origin would suggest. The planets in our sample have a wider range of compositions compared to stellar equivalent values, that could indicate formation pathways away from primordial or be the result of random scattering owing to current mass-radius uncertainties as we recover the observed outliers in mock population analysis $\sim15\%$ of the time. To truly determine whether the origin is primordial with a 1:1 true relation, we find that sample of at least 150 planets is needed and that stars that are iron enrich or depleted are high value targets.

Figures (13)

• Figure 1: Refractory ratio of stars compared to their exoplanets as populations. The host stars population is shown in red at contours of 1 and 2 $\sigma$ values, while the dotted contour corresponds to the GALAH stellar population. The marginal distribution of Fe/Mg and Fe/Si are shown outside of the scatter plot for stars (red), all exoplanets (blue) and GALAH (dotted) populations. Exoplanets above the RTR, which require volatiles, are indicated as white circles and solar system objects are shown in yellow. Notice the axes are in logarithmic scale.
• Figure 2: Exoplanet's iron-mass fraction (Fe-MF$_{pl}$) compared to the stellar [Fe/H] (top panel), [Mg/H] (middle panel) and [Si/H] (bottom panel) abundances. The results of our linear best-fit (assuming weighted sample) are shown as blue contours at 1 and 2 $\sigma$ confidence values. Similarly, exoplanets that are above RTR are indicated as white circles, while 55-Cnc e is a dotted white circle.
• Figure 3: Comparison planets' composition to their stars. Left: Planetary masses and radii in our sample with host stars planet equivalent values as a population shown in red. Right: Direct comparison of iron-mass fraction of stars (Fe-MF$_{st}$) and iron-mass fraction of planets (Fe-MF$_{pl}$), including our linear best-fit (assuming weighted sample) shown as blue contours at 1 and 2 $\sigma$ confidence values. The dashed lines are the ODR best-fit results provided by studies Adibekyan2021 (purple), Adibekyan2024 (green) and Brinkman2024 (orange). Our data and methodology is consistent with a 1:1 compositional relation between planets and stars (Fe-MF$_{pl}$=Fe-MF$_{st}$) shown as a dashed black line, we summarize our best-fit solutions in table \ref{['tab:coef_ext']}. We use the same color scheme for each star-planet pair as before.
• Figure 4: Normalized density as a function of stellar iron-mass fraction (Fe-MF$_{st}$, top panel) or stellar metallicity ([Fe/H], bottom panel). We use the same color scheme for each star-planet pair as before and show the best-fit results as blue contours at 1 and 2 $\sigma$ confidence values. For these fits we exclude planets that are not presumably rocky (i.e. unweighted sample of planets with $\rho/\rho_\oplus>0.8$).
• Figure 5: Host star iron-mass fraction equivalent (Fe-MF$_{st}$) as a function of stellar refractory abundances [Fe/H] (top panel), [Mg/H] (middle panel) and [Si/H] (bottom panel). The data is color coded according to the three datasets: this work (blue circles), Adibekyan2024 (green squares) and Brinkman2024 (orange diamonds). The GALAH dataset is shown with black contours at 1 and 2 $\sigma$ confidence values.