Multi-planet system composition comparison to host star, mock population analysis

The first solids condensing out of the disk nebula are expected to form with the original chemical signature. These first solids end up forming embryos and planets, without any major compositional reprocessing, they would preserve the primordial composition. In this case the refractory ratios of planets would be similar to that of the host star. However, Mercury is an example that violates this rule, but it is unclear if this small planet is an extreme outlier. One possibility is to turn to exoplanets to answer this question and a fruitful approach is to focus on multi-planet systems. Multi-planet systems present a unique scenario, where all the planets in the same system should be similar to the host star, assuming no outliers and if this assumption is false, then there will be a second population of Mercury-like planets. In this study, we generate a mock data set to investigate how similar multi-planet systems and their host star are in Fe/Mg ratio, given uncertainties in their mass and radius observations. The exoplanet population we simulate, of 40 planets, has a hierarchical structure that is either similar to the stars or has a mixture model where some planets are Mercury-like (iron-enriched). We find that for our nominal uncertainty case, 10% error in mass and 5% error in radius, an information criterion test cannot reliably confirm that the mock population is similar to the stars. In this case we observe that the test will often prefer the opposite model compared to the generated data. Moreover, increasing the number of planets (100>) in the sample does not improve the confidence. We suspect that this is the result of constraints on the parameter space and that a mixture model better explains the width of the composition distribution. However, decreasing the planetary uncertainty in radius to 1% leads to a confidence greater than 90% in determining if a population is similar to stars. Thus in an unbiased sample of multi-planet systems, it seems more important to constrain the uncertainties on the planetary parameters rather than increase the sample size of the population.