The relationship between the mass of a planet and the amount of heavy elements in it’s atmosphere can potentially tell us things about how that planet formed and/or evolved. Using out solar system giant planets as an example we see that with decreasing mass, there is an increase in the amount of heavy elements it’s atmosphere contains relative to the Sun. This suggests that the giant planets formed in a different way to the Sun, which formed from a large cloud of gas under gravitational instabilities, where mass and likely distance from the Sun played a role in the amount of materials they accumulated over formation timescales.
Thus far, solar system studies have used the abundance of methane (CH4) as a proxy for the overall metallicity of the atmoshere, and exoplanet studies have used water (H2O) as this proxy with the use of Hubble Space Telescope Wide Field Camera 3 transmission spectra. Importantly, these measurement only serve as an approximation based on chemical equilibrium conditions in the atmosphere. By measuring the abundance of different materials in the same atmospheres, or of another multi-giant planet system will greatly advance our understanding of the relationship between mass and formation of giant planets.
There are a number of caveats associated with this data and apparent trend:
The data presented in the figure has been compiled from a number of sources each referenced in the data table. Each dataset is presented as the 68% confidence interval based on the retrieval, where the retrievals and parameters fit in the retrieval can be different for each value.
The linear relationship is computed by fitting a straight line in log-log space. To determine the statistical significance of the data in relation to the linear fit we compute the rho2 statistic (see Wakeford et al. 2018), which determines the improvement of fit to the data with the line compared to the average of the points. This statistic shows that while the solar system can be explained by the linear fit shown, the exoplanet data does not. Additionally, this statistic can be calculated based on the addition of each new data point, which suggests that the trend will evolve in both variance and constraint as new higher precision data is obtained.
To fully evaluate this relationship between the mass of a planet and its atmospheric metallicity understanding of the chemical conditions of the atmosphere, molecular abundances of multiple species, and high precision data is needed.
NOTE: The downloadable file was updated on Dec 11th 2018 swapping the uncertainties for Uranus and Neptune to match the figure on the page.