AC13
Planetary atmospheres from thermal tails to winds
A few fast particles can leak away, or gas can flow out collectively. Follow thermal motion through a critical wind, test its heat supply, and read how atmospheric loss reshapes a planet population.
L1
How a planet loses its atmosphere
A warm atmosphere can leak a fast particle tail or flow outward as a wind. Gravity and heating decide which calculation is useful.
L2
Calculate the escaping thermal tail
Derive the Jeans flux from a velocity-weighted Maxwellian, locate an illustrative exobase and distinguish particle fractions from surface fluxes.
L3
Build a wind through its sonic point
Derive the isothermal Parker equation, choose its accelerating critical branch and compare the finite-radius heat requirement with stellar XUV power.
L3
Solve and check a critical atmospheric wind
Run a standalone Python critical-wind benchmark, compare a regular ODE integration with Lambert-W branches and diagnose failed physical assumptions.
L4
Read the competing explanations of the radius valley
Read fixed primary papers on photoevaporation, interior cooling and coupled winds, distinguishing observed populations from simulations.
Sources and calculation scope
- Cranmer 2004, New views of the solar wind with the Lambert W function, v1
7June2004; AJP 72,1397–1403. Full text, SectionsIII–IV, equations12–16: isothermal momentum equation, critical point and the two real Lambert-W branches. The solar ionized-hydrogen sound-speed convention is replaced by our explicitly fixed single-particle mass.
- Volkov et al. 2011, Thermally driven atmospheric escape, arXiv v1
26September2010 preprint, published ApJL729,L24(2011). Full text, Section 2 and Figures1–5: hard-sphere mean free path, radius-based versus local scale-height Knudsen numbers, kinetic escape and conditional Jeans corrections. Their heating below the lower boundary differs from a globally maintained isothermal wind. The adopted Lab collision cross section is a teaching input, not their molecular-nitrogen value.
- Murray-Clay, Chiang & Murray2009, Atmospheric escape from hot Jupiters, v2
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.
- Owen & Wu 2017, The evaporation valley in the Kepler planets, v2
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.
- Ginzburg, Schlichting & Sari 2018, Core-powered mass loss, v2
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.
- Misener et al. 2026, Bolometric–photoevaporative transition, v2
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.