--- title: "Read the competing explanations of the radius valley" description: "Read fixed primary papers on photoevaporation, interior cooling and coupled winds, distinguishing observed populations from simulations." canonical_url: "https://sandboxphysics.com/stories/atmospheric-escape/radius-valley/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/atmospheric-escape/radius-valley/" last_modified: "2026-10-28" --- [Planetary atmospheres from thermal tails to winds](https://sandboxphysics.com/stories/atmospheric-escape/) AC13 · L4 # Read the competing explanations of the radius valley Sandbox Physics · 2026-10-28 The radius valley is a shortage of certain intermediate-size close-in planets. Both XUV-driven loss and cooling-assisted, bolometrically heated outflows can shape it. Read how a paper connects an individual atmospheric flow to a changing planet and then to a population. ## Before you begin The preceding wind chapter distinguishes transport from available power. Open the fixed paper versions in Sources; Figure numbers below refer to those versions, not an automatically updated PDF. ## Start with a population, not a single escaping planet A radius histogram counts planets in size intervals. Before explaining a dip, ask which planets could have been detected and how stellar-radius uncertainties propagate into planet radii. A model histogram requires an initial distribution, ages and selection assumptions as well as an escape prescription. Open Owen & Wu 2017 version 2. Section 2.2 organizes the evolution around how long an envelope survives. Figure 6 shows synthetic distributions from the model. Follow what happens near the envelope thickness that makes mass loss slowest: a thin gas layer can greatly enlarge an observed radius, so removing a modest gas mass can move a planet a long way across a radius histogram. Write beside the figure which curves are generated populations and where the observed valley enters the comparison. A successful histogram is evidence about a model’s ability to reproduce a pattern; identifying a unique heat source requires more information. Reading: Owen & Wu 2017, The evaporation valley in the Kepler planets, v2 ## Follow the alternative energy reservoir Now read Ginzburg, Schlichting & Sari 2018 version 2, Section 2.1 and equations5–7. The cooling planet and envelope supply an energy reservoir, while escaping gas must still pass through an atmosphere and its transport limit. Trace the mass, radius and temperature symbols before comparing rates. Figure 1 is a calculated population with chosen parameters and age; Figure 3 brings the calculated distribution alongside the observed population. Figure 5 changes temperature. Before reading the plotted shift, predict whether temperature changes binding, transport or both. The phrase core-powered compresses a larger physical picture. Cooling helps maintain an extended atmosphere, and stellar bolometric irradiation can maintain the outer thermal structure. In a coupled calculation, the interior and the irradiated wind belong to the same evolving planet. Treat the location of the sonic surface and of radiation absorption as physical questions. Reading: Ginzburg, Schlichting & Sari 2018, Core-powered mass loss, v2 · Misener et al. 2026, Bolometric–photoevaporative transition, v2 ## Open the coupled calculation at its radial profiles Use Misener and colleagues, arXiv $2605.02766$ version 2, submitted6August2026; its PDF header is7August. The archive marks it accepted by ApJ. Sections2 and3.2 connect analytic scales with AIOLOS radiation-hydrodynamic simulations. These profiles are simulated. They are not reconstructed temperature or density measurements from a particular exoplanet. Begin with Figure 2. Read the caption’s mass, equilibrium temperature and transit radii, then locate the diamond marking the sonic radius on each velocity curve. Move upward to the heating and composition panels at that same radius. Ask whether the XUV heating reaches the subsonic flow. Figure 3 changes UV luminosity while retaining the planet parameters, providing a controlled comparison. Reading: Misener et al. 2026, Bolometric–photoevaporative transition, v2 ## Read a rate curve after identifying its radii Figure 4 compares three masses. The blue simulation points, negligible-UV comparison points and analytic curves are different calculations. Its two energy-limited approximations differ in whether the XUV absorption radius is set equal to the transit radius. Because the absorbed area depends on the square of absorption radius, that choice can matter greatly. Figure 5 holds each labeled radius fixed while changing incident XUV luminosity. Large-radius cases can be almost insensitive to it; smaller-radius cases respond, and some intermediate cases are nonmonotonic. Locate the sonic-density, radius and sound-speed factors in $\dot M=4\pi r_{\rm s}^2\rho_{\rm s}c_{\rm s}$ before interpreting that behavior. A single temperature–flux rule would miss changes of composition and density structure. For a reading exercise, draw three empty columns on paper: calculated quantity, independent input, coupled response. Put transit radius, absorption radius, temperature profile and escape rate in the appropriate columns for one plotted experiment. Then repeat for a different experiment where the planet evolves. A symbol’s role can change between experiments. Reading: Misener et al. 2026, Bolometric–photoevaporative transition, v2 · Murray-Clay, Chiang & Murray2009, Atmospheric escape from hot Jupiters, v2 ## Choose a next test that can distinguish histories The wind equations alone do not predict an entire radius distribution. You also need planet contraction, composition, initial envelope fractions, stellar irradiation history and observing selection. A numerical wind at a prescribed temperature is a useful component for understanding this chain. A productive next comparison would ask how the proposed population changes with age, irradiation or planet mass after the same selection is applied. Name the measured quantity, the model prediction and the uncertain inputs before choosing a preferred explanation. Keep present-day escaping gas separate from a claim about all the gas lost over billions of years. These papers make concrete different links in the chain: an envelope-loss timescale, a cooling reservoir, and coupled atmospheric profiles. Reading them together turns a histogram dip into a set of physical calculations and testable population questions. Reading: Owen & Wu 2017, The evaporation valley in the Kepler planets, v2 · Ginzburg, Schlichting & Sari 2018, Core-powered mass loss, v2 · Misener et al. 2026, Bolometric–photoevaporative transition, v2 ## Exercises and explanations 1. A model reproduces a radius histogram with no XUV-driven loss. Has it shown that XUV heating is absent from real planets? Read the explanation It has shown that the model can produce that population pattern under its inputs. Other mechanisms can produce similar patterns, and the coupled calculation allows several heat sources. Discrimination requires a prediction that differs after initial-condition and selection uncertainties are considered. 2. An energy-limited estimate takes $R_{\rm XUV}=R_{\rm b}$. If the absorption radius is twice as large while the binding radius and all else stay fixed, how does its rate change? Read the explanation The intercepted area becomes four times larger, so that simplified rate becomes four times larger. If the binding radius or thermal structure changes too, those changes must be included separately. ## Try the prediction ### [Isolate one step in the paper’s argument](https://sandboxphysics.com/labs/planetary-atmospheric-escape/) 1. Use the default and change only XUV power. Identify which quantities stay prescribed in this simplified comparison. 2. Compare that behavior with Figure 3 of the fixed2026 paper, where temperature and composition respond to radiation. 3. Explain which additional equations would be needed before the interactive calculation could predict a radius-valley population. [Previous: Solve and check a critical atmospheric wind](https://sandboxphysics.com/stories/atmospheric-escape/solve-a-wind/) ## Sources and calculation scope 1. [Murray-Clay, Chiang & Murray2009, Atmospheric escape from hot Jupiters, v2](https://arxiv.org/pdf/0811.0006v2) 18November2008 revision, ApJ 693,23(2009). Full text, Section 3.2, equations19/22 and Figure 7: absorbing area, energy-limited scaling and the cooling/recombination limitations of a fixed efficiency. This source develops hot-Jupiter radiation hydrodynamics; the small-planet illustration uses only the explicitly stated global power comparison. 2. [Owen & Wu 2017, The evaporation valley in the Kepler planets, v2](https://arxiv.org/pdf/1705.10810v2) 4October2017 revision; ApJ 847,29. Full text consulted, Section 2.2 erosion timescale and Figure 6 synthetic population distributions. The predicted valley is a model outcome conditioned on initial envelopes and irradiation histories, not a directly imaged escaping atmosphere. 3. [Ginzburg, Schlichting & Sari 2018, Core-powered mass loss, v2](https://arxiv.org/pdf/1708.01621v2) 6March2018 revision; MNRAS 476,759–765. Full text, Section 2.1, equations5–7, Figures1/3/5: the cooling reservoir, energy and transport limits, synthetic radius distributions and their comparison with the observed population. 4. [Misener et al. 2026, Bolometric–photoevaporative transition, v2](https://arxiv.org/pdf/2605.02766v2) arXiv version 2 submitted6August2026; PDF draft header7August2026, archive marks accepted ApJ, related DOI10.3847/1538-4357/ae969c. Full PDF consulted, Sections2 and3.2, Figures2–5. These are AIOLOS radiation-hydrodynamic simulation profiles and rates, not observed planet profiles. This course reads the fixed figures; it does not reproduce the code or its evolution calculation.