A critical assessment of the applicability of the energy-limited approximation for estimating exoplanetary mass-loss rates

Abstract

Context: The energy-limited (EL) atmospheric escape approach is used to estimate mass-loss rates for a broad range of planets that host hydrogen-dominated atmospheres as well as for performing atmospheric evolution calculations. Aims: We aim to study the applicability range of the EL approximation. Methods: We revise the EL formalism and its assumptions. We also compare its results with those of hydrodynamic simulations, employing a grid covering planets with masses, radii, and equilibrium temperatures ranging between 1 $M_{\oplus }$ and 39 $M_{\oplus }$, 1 $R_{\oplus }$ and 10 $R_{\oplus }$, and 300 and 2000 K, respectively. Results: Within the grid boundaries, we find that the EL approximation gives a correct order of magnitude estimate for mass-loss rates for about 76% of the planets, but there can be departures from hydrodynamic simulations by up to three orders of magnitude in individual cases. Furthermore, we find that planets for which the mass-loss rates are correctly estimated by the EL approximation to within one order of magnitude have intermediate gravitational potentials as well as low-to-intermediate equilibrium temperatures and irradiation fluxes of extreme ultraviolet and X-ray radiation. However, for planets with low or high gravitational potentials, or high equilibrium temperatures and irradiation fluxes, the approximation fails in most cases. Conclusions: The EL approximation should not be used for planetary evolution calculations that require computing mass-loss rates for planets that cover a broad parameter space. In this case, it is very likely that the EL approximation would at times return mass-loss rates of up to several orders of magnitude above or below those predicted by hydrodynamic simulations. For planetary atmospheric evolution calculations, interpolation routines or approximations based on grids of hydrodynamic models should be used instead.

12 pages, 7 figures, Published in A&A in June 2021; Revised on 9.11.2021 to correct typo in equation 2

References in corpus (19)

• Improved Age Estimation for Solar-Type Dwarfs Using Activity-Rotation Diagnostics
• Atmospheric Escape from Hot Jupiters
• Roche lobe effects on the atmospheric loss of "Hot Jupiters"
• Planetary population synthesis coupled with atmospheric escape: a statistical view of evaporation
• Planetary Candidates Observed by Kepler VI: Planet Sample from Q1-Q16 (47 Months)
• The active lives of stars: a complete description of rotation and XUV evolution of F, G, K, and M dwarfs
• The Extreme Ultraviolet and X-Ray Sun in Time: High-Energy Evolutionary Tracks of a Solar-Like Star
• Heating efficiency in hydrogen-dominated upper atmospheres
• Aeronomical constraints to the minimum mass and maximum radius of hot low-mass planets
• Hydrogen dominated atmospheres on terrestrial mass planets: evidence, origin and evolution
• Hydrodynamic simulations of captured protoatmospheres around Earth-like planets
• X-ray irradiation and evaporation of the four young planets around V1298 Tau
• High-energy irradiation and mass loss rates of hot Jupiters in the solar neighborhood
• Coupling thermal evolution of planets and hydrodynamic atmospheric escape in MESA
• Close-in sub-Neptunes reveal the past rotation history of their host stars: atmospheric evolution of planets in the HD3167 and K2-32 planetary systems
• The Kepler-11 system: evolution of the stellar high-energy emission and {initial planetary} atmospheric mass fractions
• Photo-evaporation of close-in gas giants orbiting around G and M stars
• The Bimodal Distribution in Exoplanet Radii: Considering Varying Core Compositions and ${\mathrm{H}}_2$ Envelope's Sizes
• Hot Super-Earths with Hydrogen Atmospheres: A Model Explaining Their Paradoxical Existence

Cited by in corpus (24)

• Irradiation-driven escape of primordial planetary atmospheres II. Evaporation efficiency of sub-Neptunes through hot Jupiters
• Irradiation-driven escape of primordial planetary atmospheres I. The ATES photoionization hydrodynamics code
• Zodiacal Exoplanets in Time (ZEIT) XIII: Planet Orbits and Atmospheres in the V1298 Tau System, a Keystone in Studies of Early Planetary Evolution
• The influence of host star activity evolution on the population of super-Earths and mini-Neptunes
• Planetary evolution with atmospheric photoevaporation II: Fitting the slope of the radius valley by combining boil-off and XUV-driven escape
• The three regimes of atmospheric evaporation for super-Earths and sub-Neptunes
• KELT-9 as an eclipsing double-lined spectroscopic binary: a unique and self-consistent solution to the system
• The Maximum Mass-Loss Efficiency for a Photoionization-Driven Isothermal Parker Wind
• Eta-Earth Revisited II: Deriving a Maximum Number of Earth-like Habitats in the Galactic Disk
• Role of Planetary Radius on Atmospheric Escape of Rocky Exoplanets
• Blowin' in the non-isothermal wind: core-powered mass loss with hydrodynamic radiative transfer
• Born Dry or Born Wet? A Palette of Water Growth Histories in TRAPPIST-1 Analogs and Compact Planetary Systems
• The Diffusion Limit of Photoevaporation in Primordial Planetary Atmospheres
• Stellar rotation and its connection to the evolution of hydrogen-dominated atmospheres of exoplanets
• The strongly irradiated planets in Praesepe
• Is the high-energy environment of K2-18b special?
• Characterizing the bolometric-photoevaporative transition in young sub-Neptunes with radiation-hydrodynamic simulations
• Gas-depleted planet formation occurred in the four-planet system around the red dwarf LHS 1903
• How black hole activity may influence exoplanetary evolution in our Galaxy
• Constraining stellar rotation and planetary atmospheric evolution of a dozen systems hosting sub-Neptunes and super-Earths
• Evolution of Mercury's Earliest Atmosphere
• Revising core powered mass loss: A critical assessment of the "energy limited" argument
• Probing habitable regions with SRG/eROSITA
• ExoplANETS-A: A VO database for host stars and planetary systems: The effect of XUV on planet atmospheres