In our solar system, there are no planets between the size of Earth and Neptune and none reside inside Mercury's orbit. Yet the Kepler mission (2009-2013) found thousands of such planets orbiting other stars, and we now know there are roughly 70 such planets per 100 Sun-like stars . During the decade since Kepler discovered these planets in such abundance, I've been fascinated by a collection of questions surrounding these Earth- to Neptune-size objects: What are they made of? Why are they so common? Why does our solar system lack such planets? In this post, I'll describe a survey that I led to attempt to answer some of these questions. I've linked a paper describing the details which will appear in The Astronomical Journal.
Context. During the early days of the Kepler mission, there was a lively debate around what to call these small planets. Some liked the term "super-Earth" because they were bigger than Earth; others preferred "sub-Neptune" because they were smaller than Neptune (which is about 4x Earth-size or 4 Re). Of course, this is just a difference in semantics, but these names evoke different ideas about the nature of these planets. A "super-Earth" sounds like a scaled up version of the Earth—a rocky body with a thin or non-existent atmosphere, while "sub-Neptune" brings to mind a scaled-down version of Neptune—a rock/ice core surrounded by a thick gaseous envelope. The media seemed to love "super-Earth," but which was closer to reality?
As Kepler discovered these super-Earths/sub-Neptunes, several groups labored to measure their masses using the Doppler method. Planet mass can be combined with planet size measured from the transit technique to constrain planet density and bulk composition. Thanks to these Doppler efforts, around 2015 we learned that most close-in planets above ~1.7 Re tended to have thick gaseous envelopes and smaller planets were mostly rocky [2,3,4 ]. So ~1.7 Re seemed to be a dividing line between super-Earths and sub-Neptunes.
However, at the time, when we plotted the tabulated planet radii, we just saw a continuum of sizes between 1 and 4 Re. There was no hint that 1.7 Re was an important dividing line between two classes of planets. The picture changed when we completed a project called the California-Kepler Survey (CKS), a spectroscopic survey of over 1000 planet-hosting stars to better understand their properties . CKS was able to improve the uncertainties on planet radii from ~40% to ~10% . What originally appeared as a single continuum of planet radii was, in fact, two separate populations of planets separated by a region of low planet occurrence . This is known as the "Radius Gap" or "Fulton Gap" and has been observed in a number of subsequent analyses of planets from Kepler mission [e.g., 8, 9].
Left: planet size and orbital period from Mullally et al. (2016). Planet sizes relied on stellar sizes based on photometry which resulted in 40% uncertainties. Right: same as left, but stellar radii are derived from spectra that achieved 10% uncertainties in planet size. A single population of planets split into two.
Theory: Even before the Radius Gap had been clearly observed, several groups had predicted the Radius Gap would exist as a consequence of "photoevaporation": atmospheric loss due to X-ray and extreme ultraviolet (XUV) radiation [e.g., 10,11]. Photoevaporation was found to be a threshold process, i.e., either negligible or complete for a given planet. Thus, photoevaporation herds young planets into distinct populations, as shown in the movie below.
Despite these successes, it's too early to be confident that photoevaporation theory is correct. An alternative class of theories has been proposed where the energy that unbinds the gaseous envelope comes not from external XUV radiation, but from the gradual cooling of the solid core. These "core-powered" models are equally successful in reproducing the Radius Gap [12,13]. (There are other models that do not rely on mass-loss [14,15]).
Movie showing planet population evolving for 300 million years under the physics of photoevaporation. Credit: Erik Petigura and James Owen.
Testing the models. So which model is right? For a given planet, the core-powered and photoevaporation models can predict the amount of envelope the planet should lose given its mass, orbital period, and host star properties. At a given orbital period and planet mass, the core-powered model predicts less mass-loss around low-mass stars, while the photoevaporation model predicts little variation with stellar mass. All else being equal, we would expect significant variation in the size of super-Earths and sub-Neptunes with stellar mass in the core-powered model.
BJ Fulton and I looked for variation with stellar mass in the CKS sample in 2018. We found some evidence that the sub-Neptunes grow with stellar mass, but the trend was subtle due to the limited range of stellar masses probed by CKS, roughly 0.8–1.4 Solar-masses or 0.8–1.4 Msun. To test these stellar mass-dependent predictions further, I designed a follow-on survey to CKS called "CKS-Cool" to augment the sample with low-mass stars ranging from 0.5–0.8 Msun. NASA and Caltech generously provided the time to conduct this survey at the Keck Telescope.
Left: Stellar mass and metallicity for stars in CKS-I and CKS-Cool. Right: same as left but showing temperature and radii.
Augmenting this survey was not as simple as gathering new spectra and applying our existing spectroscopic techniques. One of the reasons why the original CKS survey "CKS-I" did not extend below 0.8 Msun is that extracting information from spectra of these stars is challenging because they contain dense a forest of molecular lines which are difficult to model. In preparation for the project, I worked with a Sam Yee (then a Caltech undergrad, now a Princeton grad student) to build an open-source package called SpecMatch-Empirical to side-step some of the modeling challenges by using empirical spectra.
Segments of spectra containing the Mg I b triplet for seven representative stars from CKS-Cool. The red lines are our SpecMatch-Empirical fits.
Sharpening the Radius Gap. With the spectra in hand, we combined the two samples and looked for patterns in the extended sample (CKS-I + CKS-Cool). Before digging into stellar mass, it's fun take a look at some of our favorite visualizations of the population population. In the 5 years since we discovered the Radius Gap, we've refined how we measure planet radii incorporating data from the Gaia spacecraft and new light curve fitting techniques. The panels below show the planet population in period-radius space after further improving the planet radii from 10% to 5% precision. It's encouraging that the super-Earth/sub-Neptune populations continues to sharpen up.
Left: planet sizes and orbital period from CKS-I . Right: same as left, but after adding in CKS-Cool and refining planet radii from ~10% to 5% uncertainties shown as vertical bars. Note: in both plots, the contours convey the relative concentration of planets in the period-radius plane. The left panel shows the de-biased occurrence, while the right panel shows the detections.
Trends with stellar mass. We found that the sub-Neptunes grow with stellar mass while the super-Earths do not. The left panel below shows the raw sample of planets from our survey. We checked that selection effects and other confounding variables did not falsely produce this trend and the show the de-biased trends on the right panel. The average size of a sub-Neptune increases from 2.1 to 2.6 Re over a range of stellar masses spanning 0.5-1.4 Msun.
Left: planet size and stellar mass (detections only). Right: average size of super-Earths and sub-Neptunes (corrected for selection effects).
Recall that the core-powered model predicted a variation with stellar mass, while photoevaporation did not. So can we conclude that the core-powered model is correct and rule out photoevaporation? Well... Not quite.
Those predictions assumed that the planet masses themselves are independent of stellar mass. If we relax those assumptions, then the photoevaporation model can also produce the increasing slope. In fact, the proponents of both models recently teamed up and showed through simulations how closely both models can match the observed Kepler population (and each other) given the right distribution of planet masses . Since only a handful of small Kepler planets have precisely measured masses, this flexibility is allowed given the data.
What seems to be clear from our observations is that stars efficiently produce cores up to a certain threshold mass of about 10 Earth-masses or 10 Me. This not a hard boundary and Nature does produce the occasional giant planet with 20 Me of rocky material. However, most cores lie at or below this value. This threshold planet core mass appears to vary with stellar mass. Around the least-massive stars in our sample this boundary is ~5 Me, while for the most massive stars it's more like ~14 Me. Building a complete picture of planet formation requires that we understand why Nature favors planet cores below a certain threshold mass and why it's related to the mass of the host star.
Trends with stellar metallicity and age. While measuring the masses of our stars, we also measured their ages and metallicities (i.e. enrichment in heavy elements). The figures below show the super-Earth and sub-Neptune populations as a function of stellar metallicity and age. The lines show the predictions from the core-powered models  but the photoevaporation models make similar predictions. We found no correlation with metallicity. The absence of the predicted trend suggests a modification to both models is needed (namely their treatment of opacities), but does not rule either out. We also measured the dependence on stellar age. Both models predict that sub-Neptune envelopes should contract as they cool over billion-year timescales. We observed no size-age trend, but the prediction is subtle and ages are hard to measure precisely. So it's possible that our age uncertainties are washing out a real trend. Future studies of planets with well-measured ages are critical to making progress. The sample of transiting planets around young stars is growing, and a number of recent papers have pointed out that very young planets that are less than 100 million years old seem to be inflated [see, e.g., 18].
Conclusions. In this study, we constructed a large sample of planets orbiting stars of various masses. We looked for trends with stellar mass, metallicity, and age. Our data agree qualitatively with the predictions of two leading theories to explain the super-Earth and sub-Neptune dichotomy, although both models need some modification. Discriminating between these two models is difficult due to our sparse catalog of small planet masses. Currently, it's much easier to measure the radius of typical small transiting planet than its mass. Thankfully, more mass measurements will soon be possible thanks to the arrival of ultra-stabilized spectrometers at large telescopes like MAROON-X, ESPRESSO, and the Keck Planet Finder. Stay tuned!