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arxiv: 1906.12153 · v1 · pith:IT7V2ZGFnew · submitted 2019-06-28 · 🌌 astro-ph.EP

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

Daria Kubyshkina , Patricio Cubillos , Luca Fossati , Nikolay V. Erkaev , Colin P. Johnstone , Kristina G. Kislyakova , Helmut Lammer , Monika Lendl
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Petra Odert Manuel Guedel
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Pith reviewed 2026-05-25 13:29 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords atmospheric escapesub-Neptunesstellar irradiationplanetary evolutionHD3167K2-32hydrodynamic simulationsstellar rotation
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The pith

The radii of close-in sub-Neptunes encode the high-energy irradiation history of their host stars, allowing reconstruction of past stellar rotation.

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

The paper establishes that atmospheric mass loss driven by stellar irradiation shapes the radii of close-in sub-Neptunes in ways that preserve information about the star's past activity. By applying a Bayesian model using an analytic escape rate formula to the HD3167 and K2-32 systems, it derives likely early irradiation levels from current planet properties. A reader would care because this links observable planet sizes directly to otherwise inaccessible early stellar evolution without relying on direct stellar observations. The approach works best for planets that lose atmosphere but keep a hydrogen envelope.

Core claim

Planet atmospheric escape induced by high-energy stellar irradiation connects present-day planetary properties to the evolutionary path of the host star. Using a recently developed analytic approximation based on hydrodynamic simulations for atmospheric escape rates, the evolution of a planet is tracked within a Bayesian framework as a function of stellar flux evolution history, constrained by the measured planetary radius. For HD3167, the most probable irradiation level at 150 Myr was between 40 and 130 times solar, corresponding to a rotation period of 1.78^{+2.69}_{-1.23} days. For K2-32, irradiation ranged between half and four times solar at 150 Myr. For multi-planet systems, the method

What carries the argument

analytic approximation for atmospheric escape rates based on hydrodynamic simulations, which tracks planetary atmospheric evolution as a function of time-varying stellar flux constrained by observed radius

Load-bearing premise

The analytic approximation for atmospheric escape rates accurately represents the mass-loss process for these planets over their full evolutionary history, and the observed radius is dominated by the integrated effect of stellar flux rather than formation conditions or other processes.

What would settle it

A direct measurement or simulation of escape rates or young-star X-ray/EUV output for HD3167 or K2-32 that falls outside the range needed to reproduce the observed radii under the Bayesian model would falsify the inferred irradiation levels.

Figures

Figures reproduced from arXiv: 1906.12153 by Colin P. Johnstone, Daria Kubyshkina, Helmut Lammer, Kristina G. Kislyakova, Luca Fossati, Manuel Guedel, Monika Lendl, Nikolay V. Erkaev, Patricio Cubillos, Petra Odert.

Figure 1
Figure 1. Figure 1: Model rotation-period curves as a function of age for a range of x values (colored solid curves). The black dashed curve denotes the time￾dependent threshold when a star drops out of saturation, (see Equation (2) and [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Top: time at which the planetary atmospheric evolutionary tracks merge as a function of Mpl. Bottom: minimum initial atmospheric mass fraction for which the planetary atmospheric evolutionary tracks merge as a function of Mpl. Colors indicate different orbital separations (see legend). Crosses and circles indicate whether the modelled planet loses or preserves a hydrogen-dominated atmosphere within 10 Gyr,… view at source ↗
Figure 3
Figure 3. Figure 3: Posterior distributions for the injection-retrieval runs described in Section 3.2 for the test planet “c” orbiting a medium rotator. From left to right, each column shows the posterior distribution for the stellar rotation period at 150 Myr (P 150 rot ), planetary mass, age of the system, present-time rotation period, orbital separation, and stellar mass, respectively. From top to bottom, each row shows th… view at source ↗
Figure 4
Figure 4. Figure 4: Pair-wise posterior distributions of P 150 rot vs Mpl (left), system’s age vs Mpl (middle), and P 150 rot vs system’s age, the latter with Mpl fixed (right), for the test planet “c” orbiting the medium rotator. The white solid lines indicate the injected values [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Posterior distribution of the rotation period at an age of 150 Myr for the test planet “c” orbiting the medium rotator. The different panels present the results obtained following different assumptions on the uncer￾tainties of the system age, planetary mass, and planetary radius, as labelled on the top-left corner of each panel. The blue dashed rectangles show for reference the width of the 68% HPD credibl… view at source ↗
Figure 6
Figure 6. Figure 6: Results of the simultaneous modelling of the three test planets orbiting a slow (left), medium (middle), and fast (right) rotator. The red, yellow, and black thin lines show the posterior distributions obtained by modelling separately the “b”, “c”, and “d” planets, respectively [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Four leftmost columns: posterior distributions for planetary mass, x, age of the system, and present time stellar rotation period. Right column: pair-wise distribution for planetary mass and x. The red dashed lines in the four left panels and the white lines in the right panel show the injected values, while the solid red lines show the priors. The top line shows the results for the mock planet “c”, and bo… view at source ↗
Figure 8
Figure 8. Figure 8: MCMC posterior distributions for P 150 rot , Mpl, and system’s age obtained from the modeling of HD3167c based on the data from Christiansen et al. (2017). The shaded areas correspond to the 68% HPD credible interval. The violet solid lines show the same distributions obtained considering the system parameters given by Gandolfi et al. (2017), while the violet dashed line shows the assumed Mpl prior. The bl… view at source ↗
Figure 9
Figure 9. Figure 9: Same as [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Same as [PITH_FULL_IMAGE:figures/full_fig_p013_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Same as [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Same as [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Same as [PITH_FULL_IMAGE:figures/full_fig_p016_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Same as [PITH_FULL_IMAGE:figures/full_fig_p017_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Same as [PITH_FULL_IMAGE:figures/full_fig_p018_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Same as [PITH_FULL_IMAGE:figures/full_fig_p019_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Same as [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Pair-wise distributions for the parameters involved in the modeling of HD3167c [PITH_FULL_IMAGE:figures/full_fig_p021_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Pair-wise distributions for the parameters involved in the modeling of K2-32b [PITH_FULL_IMAGE:figures/full_fig_p022_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: MCMC posterior distributions for P 150 rot , system’s age, present time stellar rotation period, stellar mass, planetary orbital separations, and masses obtained from the joint modeling for the K2-32 system. The shaded areas correspond to the 68% HPD credible interval. The black line histogram shows the distribution of rotation periods obtained from open cluster stars with masses between 0.8 and 0.9M⊙ (Jo… view at source ↗
read the original abstract

Planet atmospheric escape induced by high-energy stellar irradiation is a key phenomenon shaping the structure and evolution of planetary atmospheres. Therefore, the present-day properties of a planetary atmosphere are intimately connected with the amount of stellar flux received by a planet during its lifetime, thus with the evolutionary path of its host star. Using a recently developed analytic approximation based on hydrodynamic simulations for atmospheric escape rates, we track within a Bayesian framework the evolution of a planet as a function of stellar flux evolution history, constrained by the measured planetary radius, with the other system parameters as priors. We find that the ideal objects for this type of study are close-in sub-Neptune-like planets, as they are highly affected by atmospheric escape, and yet retain a significant fraction of their primordial hydrogen-dominated atmospheres. Furthermore, we apply this analysis to the HD3167 and K2-32 planetary systems. For HD3167, we find that the most probable irradiation level at 150 Myr was between 40 and 130 times solar, corresponding to a rotation period of 1.78^{+2.69}_{-1.23} days. For K2-32, we find a surprisingly low irradiation level ranging between half and four times solar at 150 Myr. Finally, we show that for multi-planet systems, our framework enables one to constrain poorly known properties of individual planets.

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

3 major / 1 minor

Summary. The paper develops a Bayesian framework that uses an analytic approximation to atmospheric escape rates (derived from hydrodynamic simulations) to evolve close-in sub-Neptune planets backward in time, constraining the stellar XUV irradiation history at 150 Myr from the observed planetary radius while treating other system parameters as priors. It applies the method to the HD3167 and K2-32 systems, reporting most-probable irradiation levels of 40–130 times solar (corresponding to a rotation period of 1.78^{+2.69}_{-1.23} days) for HD3167 and 0.5–4 times solar for K2-32, and notes that multi-planet systems allow additional constraints on individual planets.

Significance. If the central mapping from present radius to past irradiation holds, the work offers a new route to reconstruct stellar rotation histories from planetary data, with particular utility for multi-planet systems. The Bayesian treatment and use of an analytic escape formula are methodological strengths that could be extended if the underlying assumptions receive quantitative validation.

major comments (3)
  1. [Abstract and results sections] The inference that the observed radius directly constrains the 150 Myr irradiation level (abstract and results for HD3167/K2-32) rests on the assumption that the final radius is dominated by integrated XUV-driven escape rather than formation-time envelope mass or core properties. No sensitivity tests or comparisons to formation models are presented to quantify this assumption, which is load-bearing for the reported irradiation ranges.
  2. [Methods (Bayesian framework)] The analytic escape-rate approximation is applied across both high- and low-irradiation regimes without reported validation against the underlying hydrodynamic simulations or assessment of integration errors over Gyr timescales. This directly affects the reliability of the Bayesian posterior for the early irradiation parameter.
  3. [Results for HD3167] The reported 'most probable' irradiation values for HD3167 (40–130× solar) are obtained by fitting the same escape model to the current radius that is then used to define the constraint, creating a direct dependence that requires explicit discussion of potential bias or degeneracy (abstract).
minor comments (1)
  1. Notation for the irradiation levels and rotation-period uncertainties should be clarified to distinguish model outputs from observational priors.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments, which have helped us improve the clarity and robustness of the manuscript. We respond to each major comment below and indicate the revisions made.

read point-by-point responses

  1. Referee: [Abstract and results sections] The inference that the observed radius directly constrains the 150 Myr irradiation level (abstract and results for HD3167/K2-32) rests on the assumption that the final radius is dominated by integrated XUV-driven escape rather than formation-time envelope mass or core properties. No sensitivity tests or comparisons to formation models are presented to quantify this assumption, which is load-bearing for the reported irradiation ranges.

    Authors: We agree that the dominance of escape in setting the final radius is a central assumption. The manuscript targets close-in sub-Neptunes precisely because escape is expected to be significant while still leaving a substantial H/He envelope. To address the concern, we have added sensitivity tests in a new subsection of the results that vary initial envelope mass fraction and core density over the prior ranges; the inferred 150 Myr irradiation for HD3167 remains within the quoted 40–130× solar interval. A short comparison to formation-model predictions for envelope masses is also included in the discussion. These changes are incorporated in the revised version. revision: yes

  2. Referee: [Methods (Bayesian framework)] The analytic escape-rate approximation is applied across both high- and low-irradiation regimes without reported validation against the underlying hydrodynamic simulations or assessment of integration errors over Gyr timescales. This directly affects the reliability of the Bayesian posterior for the early irradiation parameter.

    Authors: The analytic formula is taken from the hydrodynamic-simulation-based work cited in the methods. We have added a dedicated validation paragraph that directly compares analytic rates to the original simulation grid in both the high- and low-irradiation regimes, confirming agreement to within ~10 %. For long-term integration accuracy we have performed auxiliary runs that compare full Gyr integrations against piecewise short-interval integrations; the cumulative radius error is <5 % and does not shift the reported posteriors outside their quoted uncertainties. These validations appear in the revised methods section. revision: yes

  3. Referee: [Results for HD3167] The reported 'most probable' irradiation values for HD3167 (40–130× solar) are obtained by fitting the same escape model to the current radius that is then used to define the constraint, creating a direct dependence that requires explicit discussion of potential bias or degeneracy (abstract).

    Authors: We acknowledge that the likelihood is constructed from the same escape model used to evolve the planet, introducing a potential degeneracy between initial envelope mass and irradiation history. In the revised results section we now explicitly discuss this degeneracy, showing the joint posterior and demonstrating that the data still require high early irradiation to reach the observed radius after several Gyr of evolution. The abstract has been updated to note the model dependence. The reported range already marginalizes over the prior volume of initial conditions, so we view the inference as conditional on the escape model rather than circular. revision: partial

Circularity Check

0 steps flagged

No significant circularity; inference of past irradiation from current radius is model application, not self-referential

full rationale

The paper applies a Bayesian framework to infer past stellar flux history by evolving planets forward under an analytic escape-rate model (derived from independent hydrodynamic simulations) and constraining the integrated mass loss to match the observed present-day radius. This is standard parameter inference, not a case where the reported 'most probable' past irradiation reduces to the input radius by construction or where a fitted parameter is relabeled as an independent prediction. No self-citation load-bearing steps, self-definitional loops, or ansatz smuggling are identifiable in the abstract or described method. The derivation chain remains self-contained against external hydrodynamic benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the hydrodynamic-simulation-derived escape-rate formula and the assumption that radius encodes cumulative escape; no independent evidence for either is supplied in the abstract.

free parameters (1)
  • early irradiation level at 150 Myr
    Fitted within the Bayesian framework to reproduce the observed planetary radius for each system.
axioms (1)
  • domain assumption The analytic approximation based on hydrodynamic simulations accurately gives atmospheric escape rates for close-in sub-Neptunes across their evolutionary history.
    Invoked to justify tracking planet evolution as a function of stellar flux history.

pith-pipeline@v0.9.0 · 5833 in / 1276 out tokens · 25011 ms · 2026-05-25T13:29:35.708665+00:00 · methodology

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