Core-Powered Mass Loss: The Planet's Own Heat Strips Its Atmosphere

What it is and why it matters

Core-powered mass loss is a mechanism of atmospheric escape in which a planet loses its primordial hydrogen–helium envelope because of heat radiating out of its own interior, rather than because of radiation striking it from outside. When a rocky core of a few Earth masses assembles, gravitational binding energy is converted into heat, leaving the interior at tens of thousands of kelvin. That reservoir — of order 10⁴⁰–10⁴¹ erg, comparable to the core's gravitational binding energy — leaks outward on gigayear timescales at ~10²⁰–10²² erg/s, and its luminosity powers a wind at the base of the atmosphere.

It matters because it offers a self-contained explanation for one of the most striking features in exoplanet demographics: the radius valley. Kepler statistics revealed that close-in small planets cluster into two peaks — rocky worlds near 1.3 R⊕ and gas-enveloped worlds near 2.4 R⊕ — with a deficit between roughly 1.8 and 2.0 R⊕. Core-powered mass loss can carve exactly that gap: envelopes below a critical mass fraction get stripped to bare cores, while heavier envelopes survive, splitting one population in two.

The mechanism, step by step

The physics is a competition between two energy budgets and two timescales. A newborn sub-Neptune holds a puffy envelope whose base sits at the radiative–convective boundary. The escape proceeds as a transonic Parker-type wind launched near the Bondi radius, R_B ≈ GM_c μ / (k_B T), where the atmospheric thermal energy rivals the gravitational well. Gas that reaches the sonic point, R_s ≈ GM_p / (2 c_s²), streams away.

The mass-loss rate carries an exponential gate, Ṁ ∝ exp(−GM_p / c_s² R), so it is exquisitely sensitive to the sound speed c_s = (k_B T / μ)^½ — and thus to the planet's equilibrium temperature, set by total stellar flux. Two regimes emerge. For short-period planets, escape is energy-limited: the core's cooling luminosity determines whether the envelope can be unbound at all. For longer periods, it is Bondi- (time-) limited: there is enough energy, but gas trickles through the sonic point too slowly to finish within a Gyr. The interior's cooling luminosity keeps the outer envelope inflated and hot, feeding the wind until the reservoir runs dry.

Characteristic numbers, scales, and the key criterion

The controlling comparison is cooling energy versus binding energy. An envelope can be fully lost when its mass fraction is below a threshold — roughly M_atm/M_c ≲ 5% by the simplest energetic argument (and up to ~14% for γ = 7/5 in fuller treatments). Since primordial envelopes scale roughly as f ≈ 0.05 (M_c/M⊕)^½, giving a few percent for super-Earths, many planets sit right at the knife's edge, which is why the valley is sharp.

Temperatures at the radiative–convective boundary run ~10³ K (near the equilibrium temperature) for planets between Earth and Neptune, while the deep interior/core reaches ~10⁴ K, and these cores take gigayears to cool. Equating the cooling and mass-loss timescales (t_cool = t_loss) fixes the valley's shape. For Earth-like cores whose radius grows with mass as M_c ∝ R_c^β with β ≈ 4, the model predicts d log R_p / d log P ≈ −0.11, and a shift to larger planets around more massive stars of d log R_p / d log M⋆ ≈ +0.35 — both matching Kepler data. The valley itself lands near 1.8–2.0 R⊕.

How it is observed and detected

Core-powered mass loss is tested statistically, not by watching a single planet evaporate. Its fingerprints live in the precise geometry of the radius valley, which requires large, well-characterized samples. The California–Kepler Survey (CKS) sharpened Kepler radii using Keck/HIRES spectroscopy, resolving the gap; the Gaia–Kepler Survey added parallaxes for ~3,800 planets, and TESS extends the census to bright, nearby stars and to M dwarfs.

The discriminating observable is how the valley moves with host-star properties. At fixed bolometric flux, core-powered mass loss predicts essentially no shift in valley location with stellar mass (β ≈ 0.0), whereas photoevaporation predicts a negative trend (β ≈ −0.17), because XUV history depends on spectral type. Distinguishing them cleanly demands ≳5,000 planets with radius, flux, and stellar-mass uncertainties ≲5%. Complementary tests watch escape directly: metastable helium absorption at 10830 Å and Lyman-α transits probe outflow rates, and observing whether stripped cores appear around ~1 Gyr stars (rather than only very young ones) favors the gigayear core-powered clock over the ~100 Myr photoevaporative one.

Where it operates, and distinctions from related effects

The mechanism acts on close-in, low-mass planets — super-Earths and sub-Neptunes with rocky cores of about 1–10 M⊕ and thin H/He envelopes — where the escape is comparable to their formation energy. It does not strip gas giants (too deep a well) or bare rocks (nothing to lose), and it is most decisive inside a few tenths of an AU where equilibrium temperatures reach ~10³ K.

It is distinct from photoevaporation, which uses stellar X-ray/EUV photons and peaks early, and from Jeans escape, a slow thermal leak from an atmosphere's high-altitude tail that never becomes a bulk wind. Core-powered mass loss is instead a bolometrically-fed, transonic hydrodynamic outflow powered from below. Tellingly, both leading mechanisms reproduce the valley's location and 2D slope almost identically — a sign that a common energetics (unbinding a few-percent envelope from a ~1.7 R⊕ core) governs the outcome regardless of exactly which heat source does the work.

Open questions and significance

The central open question is not whether core-powered mass loss can sculpt the radius valley — it demonstrably can — but how much of the real population it shapes versus photoevaporation, and whether the two operate together or dominate in different regimes. Because their 2D radius–period slopes nearly coincide, disentangling them requires the stellar-mass and age leverage that only very large, precise surveys (and young-cluster planets from TESS and PLATO) can provide.

Deeper uncertainties remain in the inputs: the true distribution of initial envelope mass fractions from formation, core densities and compositions (which set the valley via a ρ_c^(−4/9)-type scaling), the opacity and boundary conditions that govern interior cooling, and whether the energy-limited approximation itself holds — a point recently re-examined in the literature. Resolving these will tie present-day planet radii back to their formation histories, turning the radius valley into a tool for reading how much gas planets accreted, how hot their interiors began, and how the birth environment set the boundary between rocky and gaseous worlds.

Core-powered mass loss versus stellar photoevaporation — the two leading engines that sculpt the exoplanet radius valley.

Property	Core-powered mass loss	Photoevaporation
Energy source	Planet's formation heat + stellar bolometric (total) flux	Stellar XUV (X-ray + EUV) high-energy photons
Peak epoch / timescale	Gradual, ~0.1–1 Gyr	Early, first ~100 Myr after disc dispersal
Valley slope with period	d log Rᵥ / d log P ≈ −0.11	d log Rᵥ / d log P ≈ −0.16
Valley shift with stellar mass	d log Rᵥ / d log M⋆ ≈ +0.35	Similar positive shift, but different flux dependence
Trend at fixed bolometric flux	≈ flat (β ≈ 0.0)	Negative (β ≈ −0.17)
Wind launched at	Bondi radius / sonic point, transonic Parker wind	XUV heating layer high in the atmosphere