Title: Understanding the mass-radius relation for sub-Neptunes: radius as a proxy for composition.
Authors: Lopez, E., D. and Fortney, J., J.
Affiliation: Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064
The mass-radius relationshipPanel a) of figure 1 shows the variation in radius with mass for a range of envelope fractions. The large separation between lines suggests that planet radius is a strong function of envelope fraction, at least for planets with radii greater than around 2 R⊕. Panels b) and c) demonstrate that radius is, by comparison, not a strong function of incident flux or age – the coloured lines are close together here. Based upon these results the authors suggest that planet radius depends, to first order, on the envelope fraction: radius can be used as a proxy for composition.Lets look at the bottom panel more closely – it shows that planets contract as they cool down after forming. Radius changes fairly rapidly with mass for young planets; low mass planets are actually bigger than more massive planets at the same age. This is because low-mass planets have low surface gravities, so when young and still hot are very large. Low mass planets cool fast however and therefore contract fast, rapidly reaching the same radii as the more massive planets. So after 10 billion years these planets will have the same radius, regardless of mass.The composition-radius relationshipLopez and Fortney use their thermal evolution and structure models to calculate H/He envelope fractions for the ~200 exoplanets that have both radius and mass measurements. Figure 2 shows the tight relation between calculated composition and measured radii of these planets.The composition-mass relationshipThe authors recast the mass-radius relation as a mass-composition relation and plot composition vs mass for the same 200 planets in Figure 3. The relation between composition and mass reveals something about the way planets form. Below about 10 M⊕ only 5% of a planet’s mass resides in its envelope, so there is no strong dependence of envelope fraction on mass. At greater than 10 M⊕ however, planet cores can be massive enough to trigger runaway accretion during the formation process, gathering substantial envelopes. In this sub-Neptune to gas giant regime, the relation between composition and mass becomes significant.
When do planets form envelopes: super-Earth or Sub-Neptune?What is the difference between a super-Earth and a sub-Neptune? Lopez and Fortney’s proposed definition is that sub-Neptunes have a substantial gaseous envelope, whereas super-Earths do not. But where does the boundary fall? At what planet radius can you be confident (inasmuch as you ever can be) that a planet has no envelope and at what radius can you be confident that it does? The authors suggest that super-Earths cannot be larger than 2 R⊕ (after this point a planet would certainly accumulate a substantial envelope during formation) and, realistically, any planet between 1.75 – 2 R⊕ is likely to be a sub-Neptune. On the other side of the boundary, a planet with radius less than 1.5 R⊕ is unlikely to have a substantial H/He envelope – the surface gravity on such a planet would be too low to prevent photoevaporation.
How do the results tie in with planet formation theory?The authors contextualise this work in terms of previous radius occurrence distribution studies such as those of Fressin et al (2013) and Petigura et al (2013), who find a rapid decline in planets with radii greater than 3 R⊙. According to Lopez and Fortney, this is equivalent to finding few planets with substantial envelope fractions. Large envelopes are thought to be formed by the accretion of gas from the circumstellar disk when the planetary system is still very young. When stars reach the main sequence a stellar wind sweeps circumstellar gas and dust out of the planet-forming region, stunting the growth of gaseous envelopes. It is therefore hard to form planets with extremely large envelopes, so this result nicely agrees with planet formation theory. The work presented in this paper provides a new interpretation of planet radius that allows one to indirectly probe the composition distribution of exoplanets and has exciting implications for the field of planet formation theory.* Visit exoplanets.org for a regularly updated count of all confirmed exoplanets.