Core-Powered Mass Loss in Exoplanets

• Core-powered mass loss is a hydrodynamic process where a planet’s own cooling luminosity drives the escape of its primordial H/He envelope.
• The mechanism operates through energy- and Bondi-limited regimes, balancing core energy with gravitational binding to determine mass-loss rates.
• Observational evidence, such as the exoplanet radius valley, supports CPML as a key factor shaping envelope retention and planetary demographics over gigayear timescales.

Core-powered mass loss refers to a class of hydrodynamic escape processes in astrophysical objects where mass loss is ultimately driven by energy supplied internally by the object’s core, as opposed to energy supplied externally by incident stellar radiation. In planetary science, the term primarily designates the mechanism by which the cooling luminosity from a rocky planet’s core and its deep envelope powers the spontaneous loss of its primordial hydrogen/helium atmosphere after the end of nebular accretion, thereby playing a central role in sculpting the observed bimodal distribution of small exoplanet radii—the so-called "radius valley" (Ginzburg et al., 2017, Rogers et al., 2021, Gupta et al., 2019, Gupta et al., 2021, Gupta et al., 2022, Berger et al., 2023). The concept is also applicable in stellar cluster dynamics and certain phases of massive star evolution immediately before supernova, although the focus of contemporary research is on exoplanetary envelopes.

1. Physical Principles and Regimes

Planetary systems: In the core-powered mass-loss (CPML) paradigm for close-in exoplanets, a young planet forms with a hot rocky/icy core enveloped by a modest H/He atmosphere. Upon dispersal of the gaseous protoplanetary disk, the planet is initially out of equilibrium: its core and envelope possess excess thermal and gravitational energy, which is slowly radiated away through the atmosphere’s radiative–convective boundary (RCB). This cooling luminosity (typically over Gyr timescales) can drive a Parker-type hydrodynamic wind capable of unbinding and removing light (~1–5% by mass) H/He envelopes if the energy flux is sufficient. Crucially, in the CPML scenario, the driver is the planet’s internal heat (plus some contribution from stellar bolometric flux), and not the star’s high-energy (XUV/EUV) photons as in photoevaporation (Ginzburg et al., 2017, Rogers et al., 2021, Gupta et al., 2019, Gupta et al., 2022).

The transition between core-powered mass loss and photoevaporation is controlled by the location of the Bondi radius ($R_B$)—the sonic point of core-powered outflow—relative to the penetration depth of XUV photons ($R_{XUV}$). Core-powered escape dominates when $R_B < R_{XUV}$, i.e., when XUV photons are deposited higher in the flow, while photoevaporation operates for $R_{XUV}<R_B$ (Owen et al., 2023).

In stellar clusters, the analogous process is the energy injection into a cluster’s potential via stellar evolution mass loss concentrated in the core, which "fuels" the cluster’s dynamical expansion (Gieles, 2012). In the late evolutionary stages of massive stars, enhanced neutrino luminosity causes direct core mass loss, which can reduce the gravitational binding of the envelope, in some cases inducing surface ejection if the Eddington limit is breached (Moriya, 2014, Shiode et al., 2013).

2. Analytical Framework and Governing Equations

The exigency of CPML is set by the competition between the planet’s available internal energy reservoir and the minimum energy required to unbind the atmosphere. The canonical simplified description is as follows:

Atmospheric escape proceeds at a rate:

$$\dot{M}_{atm}(t) = \min \left[\dot{M}_E, \dot{M}_B \right]$$

where

• $\dot{M}_E$ (energy-limited regime): $$\dot{M}_E \simeq L_{cool} / (g R_c) = L_{cool} R_c / (G M_c)$$ (all cooling luminosity $L_{cool}$ is used to drive escape against surface gravity $g$) (Ginzburg et al., 2017, Gupta et al., 2019, Rogers et al., 2021).
• $\dot{M}_B$ (Bondi-limited regime): $$\dot{M}_B = 4\pi R_s^2 c_s \rho_{rcb} \exp\left[-G M_p / (c_s^2 R_{rcb})\right]$$ (Ginzburg et al., 2017, Rogers et al., 2021).

Key parameters and relations:

• $L_{cool}$ (luminosity at RCB) is determined by radiative diffusion: $$L_{cool} = (64\pi/3) \sigma_{SB} T_{eq}^4 R'_B / (\kappa \rho_{rcb})$$ (Ginzburg et al., 2017, Rogers et al., 2021).
• The planet’s structure divides the envelope into an inner convective and outer isothermal radiative skin; $T_{eq}$ is set by stellar bolometric flux (Ginzburg et al., 2017, Rogers et al., 2021, Gupta et al., 2022).
• Mass-loss ceases when $t_{loss} = M_{atm} / \dot{M}_{atm}$ exceeds the system age.

The analytic scaling for the location of the radius valley is

$R_{gap} \propto S^\alpha M_*^\beta$

where $S$ is incident stellar bolometric flux, $M_*$ stellar mass, with exponents for CPML found to be $\alpha \simeq 0.08$ and $\beta \simeq 0.00$ (Rogers et al., 2021, Berger et al., 2023, Gupta et al., 2022).

In the isothermal Parker-wind limit, $\dot{M}_{iso} \approx 4 \pi r_s^2 \rho_s c_s$ with $r_s = G M_p / 2 c_s^2$; extensions for non-isothermal atmospheres reveal $\dot{M}$ is sensitive to the ratio $\gamma$ of visible to IR opacity, potentially varying the mass-loss rate by ten orders of magnitude depending on atmospheric composition (Misener et al., 2024).

3. Numerical Modeling and Evolutionary Outcomes

Population synthesis and coupled evolutionary ODE integration show that, for realistic compositions and initial conditions, CPML naturally reproduces the observed exoplanet radius distribution:

• Massive or cold planets retain their envelopes (sub-Neptunes; $R_p\gtrsim2\,R_\oplus$).
• Less massive or hotter planets lose their atmospheres to become bare cores ("super-Earths"; $R_p\sim1.3$–$1.5\,R_\oplus$) (Ginzburg et al., 2017, Gupta et al., 2018, Rogers et al., 2021, Gupta et al., 2019, Berger et al., 2023).

The resulting "radius valley" at $1.5$–$2.0\,R_\oplus$ is a robust feature of this physical process; its weak dependence on $T_{eq}$ and insensitivity to the host’s XUV history sets it apart from photoevaporation, providing a qualitative as well as quantitative match to the Kepler radius gap (Ginzburg et al., 2017, Rogers et al., 2021, Berger et al., 2023).

CPML remains efficient over Gyr timescales, in contrast to photoevaporation which is strongly front-loaded in the first $\sim$100 Myr of stellar evolution (Gupta et al., 2019, Gupta et al., 2022). Bayesian inference frameworks (e.g., as in (Gupta et al., 2021)) can be used to identify present-day mass-losing planets, with predicted observable mass-loss rates $10^7$–$10^9$ g/s.

The effect is sensitive to envelope and core properties; for core-dominated, thin envelopes ($f < \mu/\mu_c \sim5\%$), mass-loss is runaway and total ejection is likely. For more massive atmospheres, the cooling timescale dominates and envelopes survive (Ginzburg et al., 2017).

4. Observational Diagnostics and Demographics

Distinctive observable consequences allow for empirical assessment of whether CPML or photoevaporation dominates:

• The valley location depends only weakly on host mass and incident flux in CPML ($\beta\sim0$), but more strongly in photoevaporation ($\beta<0$) (Rogers et al., 2021, Gupta et al., 2022, Berger et al., 2023, Gupta et al., 2019).
• Analysis of the 3D space of planet radius, incident flux, and host mass confirms the CPML prediction that the slope of the gap with stellar mass is consistent with zero ($\beta_{obs}=-0.046^{+0.125}_{-0.117}$) and that with incident flux is shallow ($\alpha_{obs}=0.069^{+0.019}_{-0.023}$) (Berger et al., 2023), matching theoretical values.
• Around low-mass stars, the radius valley is narrower and less empty, again as predicted by CPML (Gupta et al., 2022).
• No detectable trends in gap location with proxies for stellar UV/XUV emission or age (after instellation detrending) further support CPML (Loyd et al., 2019, Rogers et al., 2021, Berger et al., 2023).
• Some multi-planet systems (e.g., K2-3) remain unexplained by either mechanism alone, suggesting the operation of stochastic or additional processes (Diamond-Lowe et al., 2022).

5. Current Debates, Model Uncertainties, and Extensions

Recent work has critically re-examined common modeling assumptions:

• The traditional "energy-limited" prescription for core-powered escape can substantially underestimate mass-loss rates in the post-giant-impact regime; the outflow is fundamentally determined by the hydrodynamics at the sonic point, not the planet’s instantaneous cooling luminosity (Modirrousta-Galian et al., 19 Sep 2025). For post-impact, hot, low-mass planets, CPML can remove all H atmospheres on timescales $\ll1$ Myr, vastly faster than photoevaporation.
• The role of early "boil-off" (a rapid, luminosity-driven escape phase immediately after disk dispersal) is now recognized: boil-off can remove 5–30% of an atmosphere, especially in low-mass or highly irradiated systems. Beyond this initial phase, long-lived CPML makes a negligible contribution ($\lesssim0.1\%$ by mass) to further envelope erosion and thus does not by itself carve the modern observed radius valley (Tang et al., 2024). This asserts that photoevaporation, not CPML, may set the final gap if early boil-off is always efficient.
• Atmospheric composition and radiative transfer details matter: the Parker-wind mass-loss rate is highly sensitivity to the visible/IR opacity ratio, which is determined by the specifics of atmospheric chemistry, metallicity, and cloud/haze formation. Observations of atmospheric escape thus can probe composition via this dependence (Misener et al., 2024).

6. Broader Astrophysical Contexts and Alternate Usages

Beyond exoplanets, the term "core-powered mass loss" is relevant in:

• Globular and open cluster evolution: mass lost by evolved stars in the dense core releases binding energy, sustaining self-similar expansion of the cluster so long as the energy injection rate matches the outward flux by two-body relaxation (Gieles, 2012).
• Massive pre-supernova stars: in the final years before collapse, core neutrino emission can reduce the gravitational binding enough to unbind the envelope if the star is near the Eddington limit (Moriya, 2014). "Wave-driven" (a form of core-powered) mass loss during late burning stages (via gravity waves excited by core convection) can also transport fusion energy outward and drive circumstellar ejecta that shape supernova progenitor evolution and light curves (Shiode et al., 2013).

7. Summary Table: Theoretical and Observational Discriminants

Quantity / Prediction	Core-Powered Mass Loss	Photoevaporation
Radius gap slope vs. $S$ ($\alpha$)	$\sim$0.08 [$\partial\log R_{gap}/\partial\log S$]	$\sim$0.12
Radius gap slope vs. $M_*$ ($\beta$)	$0$	$-0.17$
Age evolution of valley/gap	Continues Gyr timescales	Rapid, within $\lesssim$100 Myr
Gap depth/width for M dwarfs	Shallower, less empty, narrower	Sharper, deeper, broader
Sensitivity to XUV/host activity	None	Strong

Empirical measurements of these slopes and dependences serve as the principal observational discriminants; results from Kepler and other surveys to date support a primary role for core-powered mass loss in sculpting the close-in small exoplanet population (Berger et al., 2023, Gupta et al., 2019, Gupta et al., 2022, Rogers et al., 2021). The detailed balance among core-envelope structure, bolometric irradiation, atmospheric composition, and early thermal escape remains an active domain of research.