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arxiv: 2606.17143 · v1 · pith:KI6SDVJJnew · submitted 2026-06-15 · 🌌 astro-ph.EP

The Effect of Adiabatic Index on Radius Evolution and the Mass Loss

Arick Collander , Eve J. Lee This is my paper

Pith reviewed 2026-06-27 02:40 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords adiabatic indexexoplanet radius evolutionmass lossyoung planetsplanetary interiorsenvelope contractionthermal state
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The pith

Assuming a high adiabatic index overestimates the impact of mass loss on young exoplanet radii.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Models tracking exoplanet sizes often fix the adiabatic index at 1.4, a value fitting older planets. For planets only millions of years old, the index drops to about 1.2 due to thermodynamic conditions. Varying this index shows that higher values produce initially larger envelopes that contract more rapidly while losing mass faster. This leads to an overestimation of mass loss's role when high gamma is assumed, particularly for young worlds. The work calls for improved handling of starting thermal states in evolution calculations.

Core claim

The central claim is that envelopes with larger adiabatic indices start puffier and undergo faster radius contraction with accelerated mass loss. Therefore, assuming gamma ~1.4 overestimates the effect of mass loss in shaping the exoplanetary population, especially when young planets are considered. This arises because the lower gamma of ~1.2 for young planets changes how interior mass is distributed.

What carries the argument

The adiabatic index gamma in the planetary interior structure equations, which controls mass distribution and thereby sets the pace of radius contraction and mass loss.

If this is right

  • Envelopes with gamma equal to 1.4 begin with larger radii than those with gamma equal to 1.2 when all other parameters are held fixed.
  • Higher gamma produces faster radius contraction over time.
  • Mass loss proceeds at an accelerated rate when gamma is higher.
  • The overestimation of mass loss's role grows larger for planets younger than roughly one gigayear.
  • Evolutionary models must incorporate age-dependent initial thermal conditions to match measured radii accurately.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Current radius-valley interpretations that rely on high-gamma tracks may need revision once lower values are adopted for the first 100 million years.
  • Radius measurements from young clusters could directly constrain the effective gamma by showing whether contraction is slower than high-gamma models predict.
  • Coupling time-variable gamma with different equations of state might change the predicted timing of atmospheric escape in formation models.
  • This effect could alter estimates of how long certain planets retain thick envelopes before photoevaporation dominates.

Load-bearing premise

The claim that young planets have an adiabatic index of approximately 1.2 that applies directly within the evolutionary structure equations.

What would settle it

Direct comparison of observed radii for planets in star clusters younger than 100 million years against model tracks run with gamma fixed at 1.2 versus 1.4.

Figures

Figures reproduced from arXiv: 2606.17143 by Arick Collander, Eve J. Lee.

Figure 2
Figure 2. Figure 2: Planet radius Rpl vs envelope mass fraction Menv/Mcore for a planet with Mcore = 5M⊕, at an orbital period of 30 days, and at the age of 100 Myr. At large enough Menv/Mcore, larger γ feature larger Rpl but the radii converge to the same value at Menv/Mcore ∼ 0.16% below which lower γ show slightly larger Rpl. take τKH as the planet age. Higher γ correspond to an outwardly concentrated mass profile, so we m… view at source ↗
Figure 1
Figure 1. Figure 1: Planet radius Rpl vs planet age with Mcore = 5M⊕ at an orbital period of 30 days, with envelope mass fractions Menv/Mcore of 5%, 1%, and 0.1% from top to bottom panels. Different colors each correspond to different γ. Larger γ envelopes begin with larger Rpl but also con￾tract more quickly. At the lowest Menv/Mcore, the difference in the initial radius for varying γ is small enough that the Rpl for γ = 1.4… view at source ↗
Figure 3
Figure 3. Figure 3: Photoevaporation for a planet with Mcore = 5M⊕, Menv/Mcore = 5%, at orbital periods of 10 days (left) and 30 days (right). The rate of mass loss is higher for larger γ. At an orbital period of 10 days, γ = 1.4 envelope is completely stripped away within ∼170 Myrs with lower γ envelopes surviving over progressively longer timescales. At an orbital period of 30 days, all γ approach a radius of Rpl ≈ 2.47R⊕. … view at source ↗
Figure 4
Figure 4. Figure 4: Internal heat powered mass loss for a planet with Mcore = 5M⊕, Menv/Mcore = 5%, at orbital periods of 10 days (left) and 30 days (right). At an orbital period of 10 days, γ = 1.30, 1.35, 1.40 have large enough radii that their entire envelope is stripped away immediately and Rpl = Rcore. At an orbital period of 30 days, only γ = 1.4 is large enough to have its envelope stripped away immediately while all o… view at source ↗
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Our time evolution model with and without mass loss (photoevaporation only) compared with data from exoplanets in the NASA exoplanet archive retrieved on 2026-05-28 ( NASA Exoplanet Archive 2026). The solid lines correspond to the expected radius evolution under passive cooling without mass loss and the dashed lines correspond to that from photoevaporative mass loss. For illustration purpose, we fix the pl… view at source ↗
read the original abstract

Models that track the size evolution of exoplanets often assume a prescribed initial thermal state or a single adiabatic index to describe the planetary interior structure, the latter of which is taken to be $\gamma \sim1.4$ which is likely appropriate for evolved planets ($\gtrsim$1 Gyr). Extrapolating this high $\gamma$ to earlier ages (down to $\sim$million years old) is problematic since, according to thermodynamics, the adiabatic index of young planets is $\sim$1.2, which is low enough to drastically change how interior mass is distributed. We quantify the effect of varying the adiabatic index from 1.2 to 1.4 on the expected radius of the exoplanet over time. We find that envelopes of larger adiabatic indices start puffier with all else equal and undergo faster radius contraction with accelerated mass loss. Assumption of high $\gamma$ can therefore overestimate the effect of mass loss in shaping the exoplanetary population, especially when young planets are considered. We highlight the need for a more careful consideration of the initial thermal condition of planets in evolutionary models to properly interpret the radii measurements of exoplanets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript examines the effect of the adiabatic index γ on exoplanet radius evolution and mass loss. It argues that γ ≈ 1.4 is appropriate only for evolved planets (≳1 Gyr) while young planets have γ ≈ 1.2 according to thermodynamics; envelopes with higher γ are initially puffier, contract faster, and lose mass more rapidly. Consequently, assuming high γ overestimates the imprint of mass loss on the young exoplanet population, and the work calls for more careful treatment of initial thermal conditions in evolutionary models.

Significance. If substantiated, the result would demonstrate that planetary radius tracks and inferred mass-loss efficiencies are sensitive to the choice of γ at early ages, with direct consequences for population-level interpretations of observed radii and the relative importance of photoevaporation versus other processes in young systems.

major comments (2)
  1. [Abstract] Abstract: The central claim that 'according to thermodynamics, the adiabatic index of young planets is ∼1.2' is stated without derivation, explicit calculation (e.g., from Cp/Cv including ionization or dissociation), reference to a specific equation of state, or mapping from the thermodynamic value to the polytropic/adiabatic assumption actually solved in the evolutionary code's hydrostatic structure equations. This mapping is load-bearing for the reported radius and mass-loss differences.
  2. [Abstract] Abstract: No methods, equations, code description, numerical setup, or error analysis are provided, so it is impossible to verify whether the claimed radius-contraction and mass-loss differences between γ = 1.2 and 1.4 are robust to choices of initial conditions, grid resolution, or data selection.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight areas where the manuscript requires additional detail to support its claims. We agree that both the thermodynamic justification and the methods description are currently insufficient in the abstract and will revise the manuscript to address these issues directly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'according to thermodynamics, the adiabatic index of young planets is ∼1.2' is stated without derivation, explicit calculation (e.g., from Cp/Cv including ionization or dissociation), reference to a specific equation of state, or mapping from the thermodynamic value to the polytropic/adiabatic assumption actually solved in the evolutionary code's hydrostatic structure equations. This mapping is load-bearing for the reported radius and mass-loss differences.

    Authors: We acknowledge that the thermodynamic basis requires explicit support. In the revised manuscript we will add a dedicated paragraph deriving the effective adiabatic index from the ideal-gas relation γ = Cp/Cv, incorporating the reduction due to H2 dissociation and ionization in young, warm envelopes, citing a standard equation of state (e.g., Saumon-Chabrier or similar), and clarifying how this thermodynamic γ is adopted as the polytropic index in the hydrostatic structure solver. This addition will make the mapping transparent and substantiate the reported differences. revision: yes

  2. Referee: [Abstract] Abstract: No methods, equations, code description, numerical setup, or error analysis are provided, so it is impossible to verify whether the claimed radius-contraction and mass-loss differences between γ = 1.2 and 1.4 are robust to choices of initial conditions, grid resolution, or data selection.

    Authors: We agree the present concise format omits these elements. The revised manuscript will include a Methods section that specifies the evolutionary code, the form of the hydrostatic and energy equations solved, the adopted initial conditions (entropy, core mass, envelope mass), grid resolution and convergence criteria, and any sensitivity tests performed on initial conditions or numerical parameters. This will allow readers to assess robustness. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central result is direct numerical comparison of fixed-γ models

full rationale

The paper asserts γ≈1.2 for young planets 'according to thermodynamics' and quantifies radius evolution by running models with γ varied from 1.2 to 1.4. No load-bearing step reduces the reported radius difference or mass-loss imprint to a fitted parameter, self-citation chain, or definitional equivalence (e.g., no prediction that is the input by construction). The derivation is therefore self-contained as a set of forward evolutionary calculations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; full model equations, equation of state, and numerical implementation are unavailable, so the ledger is necessarily incomplete.

free parameters (1)
  • adiabatic index gamma
    Explicitly varied between 1.2 and 1.4 to test sensitivity; values chosen from thermodynamic expectations rather than fitted to data in the abstract.
axioms (1)
  • domain assumption Adiabatic index of young planets is approximately 1.2 according to thermodynamics
    Stated in abstract as the reason high-gamma extrapolation is problematic; no derivation or reference supplied.

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