The Radius Valley

Two kinds of small planet, and a gap between them

If you take every small planet that orbits close to its star, measure its size precisely, and build a histogram of radii, you do not get a smooth bell curve. You get a double-humped distribution: a crowd of planets at about 1.3 Earth radii, a second crowd at about 2.4 Earth radii, and a conspicuous dip between them at roughly 1.8 R⊕. That dip is the radius valley. Nature seems to dislike making close-in planets of exactly that size, even though it happily makes planets a bit smaller and a bit larger.

The two peaks are physically distinct populations. The lower hump is super-Earths — bare, rocky, iron-and-silicate worlds a little bigger than Earth, with densities consistent with no significant gas envelope. The upper hump is mini-Neptunes — rocky cores of similar mass wrapped in a thin but voluminous hydrogen-helium atmosphere that puffs them up. The startling discovery of the last decade is that these are not two unrelated kinds of object. They are very likely the same cores, sorted into two outcomes by whether or not they managed to hold onto a sliver of primordial gas.

How the gap was found: the Fulton gap

The radius valley is shallow — the bottom of the gap holds only about 30 percent as many planets as the peaks — and it is narrow. A modest error in measured planet radii smears it into oblivion. For years it was hidden in the Kepler catalogue for exactly this reason.

A transiting planet does not tell you its absolute size directly; the transit depth gives you the ratio of planet radius to stellar radius, (R_p/R_★)². So your planet radius is only as good as your stellar radius. In the original Kepler catalogue, stellar radii were uncertain by 25–40 percent, blurring planet radii to the point where the valley was invisible. The breakthrough came from the California-Kepler Survey (CKS): Benjamin Fulton, Erik Petigura and collaborators obtained high-resolution spectra of about 1,300 Kepler host stars, pinning down their temperatures, gravities and radii. Combined with the precise distances from Gaia, this drove stellar-radius errors down to a few percent and planet-radius errors to roughly 5 percent.

When Fulton et al. replotted the radius distribution of this clean sample in 2017, the gap snapped into sharp relief. It has been called the Fulton gap ever since. It was not a new theoretical idea — atmospheric escape had been predicting such a feature for years — but it was the first time the data were precise enough to see it.

Why one percent of gas doubles a planet's size

The key to the whole story is how absurdly little gas it takes to turn a rocky core into a mini-Neptune. A bare rocky planet of, say, 5 Earth masses has a radius near 1.5 R⊕. Add a hydrogen-helium envelope worth just 1 percent of the planet's mass and its observed (transit) radius can swell to ~2.4 R⊕ — because the transit measures the radius at the top of a low-density, extended atmosphere, not the solid surface.

Hydrogen and helium are light and, at the temperatures of close-in planets (700–1500 K), highly distended. A percent-level envelope forms a thick, fluffy shell that can contribute as much to the apparent radius as the entire solid core beneath it. This is why the population is bimodal rather than continuous: a planet that keeps a percent-level envelope looks like a mini-Neptune, while one that loses essentially all of it collapses to its bare rocky radius. There is no stable, long-lived configuration in between — a planet cannot maintain a tiny fraction of a percent of gas because escape runs away and removes the last of it quickly. So the 1.8 R⊕ bin between the two peaks stays empty.

The carving tool: atmospheric escape

What removes the envelope? Both leading mechanisms are forms of thermally driven atmospheric escape, in which the upper atmosphere is heated until gas in the outermost layers exceeds the escape velocity and streams away as a hydrodynamic wind. They differ in their energy source.

Photoevaporation uses the host star. Young stars are bright in X-ray and extreme-ultraviolet (together, XUV) radiation — up to ~10⁻³ of their bolometric luminosity in the first ~100 million years, declining steeply thereafter. This high-energy flux is absorbed high in a planet's atmosphere, heats it to ~10⁴ K, and drives an escaping wind. The mass-loss rate in the energy-limited approximation is

Ṁ ≈ η · π R_p³ · F_XUV / (G M_p)

where F_XUV is the incident high-energy flux, R_p and M_p are the planet's radius and mass, and η (~0.1) is an efficiency. The R_p³/M_p dependence means low-density, low-gravity planets close to the star lose mass fastest. Photoevaporation does most of its work early, while the star is XUV-active.

Core-powered mass loss uses the planet itself. A young rocky core retains substantial heat of formation and radiates it slowly (its internal luminosity). That heat flows up into the base of the envelope and, combined with the bolometric stellar irradiation keeping the outer atmosphere hot, can drive escape from the planet's own thermal reservoir — no XUV required. It operates more gradually, over ~1 billion years, coupling the planet's cooling to the slow erosion of its envelope.

Both mechanisms strip thin envelopes from small, close-in, low-gravity cores while sparing the gas of more massive or more distant planets. Both therefore predict a valley near 1.8 R⊕. Disentangling which dominates — or in what proportion — is one of the liveliest debates in exoplanet demographics.

The numbers: peaks, depth, and the period slope

Here are the headline figures that define the valley, drawn from the CKS sample and follow-up work.

Quantity	Value	Meaning
Super-Earth peak	~1.3 R⊕	Bare rocky-core radius
Valley centre	~1.8 R⊕	Scarcity dip
Mini-Neptune peak	~2.4 R⊕	Core + ~1% H/He envelope
Valley depth	~30% of peak	Not empty, just thin
Period range	P ≲ 100 days	Where escape is effective
Period slope	R_valley ∝ P−0.10	Negative — favours escape models
Envelope mass to cross	~1% of M_p	Tiny gas fraction, huge size effect

The negative period slope is the single most diagnostic number. Planets on wider orbits receive less flux, so the threshold size for stripping is slightly smaller; the valley therefore tilts down toward longer periods as roughly R ∝ P^−0.1. Crucially, this is the opposite sign from "gas-poor formation" scenarios (in which the gap reflects how much gas a planet could accrete in the disk rather than how much it later lost) — those predict a positive slope. The observed negative slope is strong circumstantial evidence that escape, not formation, sculpts the valley.

What the gap tells us about composition

Combining radius with mass (from radial velocity or transit-timing variations) gives bulk density, which is the real arbiter of composition. Across the valley, the densities tell a clean story:

• Below the valley (super-Earths, <1.5 R⊕): densities cluster around or above Earth's (5.5 g/cm³), consistent with an Earth-like iron-plus-rock mixture and no detectable gas. These are stripped cores.
• Above the valley (mini-Neptunes, ~2–3 R⊕): densities drop to ~2–3 g/cm³ and below, far too low for rock. The deficit is made up by a light hydrogen-helium envelope (or, in some interpretations, a substantial water/steam layer).
• Larger still (sub-Neptunes to Neptunes, >3 R⊕): envelopes become massive enough that the planet is safe from total stripping and sits comfortably above the valley.

This density transition coincident with the radius valley is the smoking gun: the size gap is a composition gap. A planet is either a rock or a rock with a thin gas blanket, and the valley marks the boundary between the two fates.

Famous examples on either side

• TRAPPIST-1 planets. All seven are below the valley — rocky, sub-1.2 R⊕ worlds around an ultra-cool M dwarf. They illustrate the super-Earth/terrestrial side of the divide (and show the valley shifts to smaller radii around low-mass stars).
• Kepler-36 b and c. A textbook pair in one system: an inner ~1.5 R⊕ rocky super-Earth (b) and an outer ~3.7 R⊕ low-density mini-Neptune (c) on orbits differing by only ~10 percent in distance. Nearly identical irradiation, wildly different densities — a natural experiment in why some cores keep gas and others don't.
• GJ 1214 b. The archetypal mini-Neptune (~2.7 R⊕, low density), the first sub-Neptune with a measured (flat, cloudy) transmission spectrum — squarely above the valley.
• 55 Cancri e. A ~1.9 R⊕, ultra-short-period (0.74-day) super-Earth so hot (~2700 K dayside) that any primordial envelope was long gone; a likely stripped core sitting near the valley's hot edge.
• Catching escape in the act. Planets like GJ 436 b and HD 209458 b show extended hydrogen comae and tails in Lyman-α and metastable-helium observations — direct detections of atmospheric escape, the very process that carves the valley.

Where the valley lives on the size-period diagram

The valley is not a single number; it is a curved line on the planet radius-versus-orbital-period plane. Close in (P ~ a few days), the gap sits near ~1.8 R⊕; by P ~ 100 days it has drifted slightly lower. Beyond ~100 days the irradiation is too weak and the escape too slow to have cleared the population over the system's lifetime, so the valley fades — there simply hasn't been enough time or flux to strip those planets.

The valley also responds to stellar mass. More massive (hotter, more luminous) stars deliver more flux and more XUV, so the valley sits at larger radii around them and at smaller radii around cool M dwarfs. Tracking the valley's location as a function of stellar mass and system age is now a primary tool for testing escape models, because photoevaporation (fast, early, XUV-driven) and core-powered loss (slow, billion-year, internally driven) predict measurably different age and mass dependences.

Common misconceptions and edge cases

• "The valley is completely empty." It is not. It is a ~30 percent dip, not a true void. Planets do exist at 1.8 R⊕; they are just much rarer than at the flanking peaks, and many of them may be transitional objects actively losing their last gas.
• "It's the same as the Neptune desert." Different feature. The radius valley is a thin gap at ~1.8 R⊕ spanning a wide period range; the Neptune desert is a broad scarcity of Neptune-sized planets on very short (≲4-day) orbits. They share a cause (escape) but live in different parts of the diagram.
• "Mini-Neptunes are mostly gas." No — the envelope is typically only ~1 percent of the mass. The core still dominates the mass; the gas just dominates the volume. That mass/volume split is exactly why a small amount of escape produces a large, sudden change in radius.
• "The valley proves photoevaporation." It proves thermally driven escape of some kind, given the negative period slope. It does not, by itself, settle photoevaporation versus core-powered mass loss; both fit the basic feature and the contest is decided by finer trends.
• "Water worlds are ruled out." Not entirely. Some mini-Neptune densities can also be explained by water/steam-rich compositions instead of H/He envelopes, and a "water world" interpretation predicts its own variant of the valley. Distinguishing thin-H/He from water-rich interiors is an open observational problem for missions like JWST.
• "Selection effects make the gap." Transit surveys do favour larger planets, but the valley survives careful completeness corrections and appears in independent samples. It is a real feature of the underlying population, not an artefact of detection bias.