Generating eccentricity from envelope stripping in the Radius Valley

Brad M. S. Hansen

REVIEW 4 major objections 5 minor 82 references

Generating eccentricity from envelope stripping in the Radius Valley

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The stripped envelope of a close-in planet can remain as a gas torus, excite eccentricities of order 0.1 through Lindblad resonances, and widen the period ratios of neighbouring planet pairs.

desk verdict A genuinely new mechanism for the radius-valley eccentricity signal, built on transparent angular momentum accounting, but the torus-persistence assumption is asserted rather than demonstrated and the numerical calibration has a factor-of-ten slip. read the letter →

arxiv 2608.04231 v1 pith:TIS6WCWQ submitted 2026-08-04 astro-ph.EP

Brad M. S. Hansen This is my paper · ORCID

classification astro-ph.EP

keywords radiusvalleyeccentricityexcitationenvelopestrippingLindbladresonancesgaseoustorusKeplermulti-planetsystemsperiodratiophotoevaporation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that when a close-in planet loses its gaseous envelope, the stripped gas does not always vanish: it can settle into a low-mass torus around the star. That torus absorbs angular momentum from the planet through Lindblad resonances, pumping the planet's orbital eccentricity to values around 0.1 even for envelope mass fractions of only a few percent. In multi-planet systems, the torus acts as an intermediary that transfers angular momentum outward, widening the period ratio of neighbouring pairs. The paper finds that Kepler planet pairs straddling the radius valley are about 5-10% wider in period ratio than pairs that both sit above the gap, and reads this as support for identifying planets in or near the valley as stripped cores.

What carries the argument

The central object is a tenuous, long-lived gaseous torus just outside the planet's orbit, with a width comparable to the planet's Hill sphere, formed from the stripped envelope. The dynamical engine is the excitation of outer eccentric Lindblad resonances: torques there launch waves that carry angular momentum from the planet into the gas, while saturated corotation resonances fail to damp the planet's eccentricity. The main working expression is the pumping timescale $1/t_e = G(p)\, f\, (M_p/M_*)^2\, (1 + a_p/w)^4\, \Omega$, where the saturation parameter $p \sim 2.465\,(M_p/10\,M_\oplus)^{-5/27}(\alpha/0.01)^{-1/9}(e_p/0.01)$ decides whether eccentricity grows (p > 0.157). Angular-momentum conservation between planet, torus and outer planet then gives the final period-ratio shift $P'_2/P_1 \sim (P_2/P_1)\,[1 + (3/2)(M_1/M_2)\, e_1^2/(P_2/P_1)^{1/3}]$.

What would settle it

A decisive test would be to measure eccentricities of a large, well-characterised sample of planets in and just below the radius valley: if high-precision radial-velocity or transit-duration data show e < 0.01 for these planets, or show no systematic 5-10% period-ratio excess for gap-straddling pairs when the sample is enlarged with K2 and TESS radii, the mechanism as described would be ruled out.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a new dynamical channel for the radius valley: envelope stripping itself explains the elevated eccentricities seen for planets with radii near 1.75-1.93 R⊕. The stripped envelope forms a gas torus outside the planet; outer eccentric Lindblad resonances in that torus extract angular momentum and raise e_p, with the saturated-resonance calculation yielding $e_p \sim 0.056\,(f/0.01)^{1/2}(w_f/0.3)^{1/2}$ and values above 0.1 for mass-loss fractions above about 5%. Because the torque decays as the torus is pushed outward, the process self-limits at a period-ratio expansion near 2.3. In multi-planet systems the gas is not the final sink of angular momentum but a mediator, and the resulting period-ratio shift of a few to about 10% matches the Kepler gap-straddling pairs.

Load-bearing premise

The load-bearing premise is that in most mass-losing systems the stripped envelope remains as a coherent gas torus for many dynamical timescales instead of being quickly blown away, and the paper does not quantify how often that happens.

Editorial extensions

If this is right

Planets that have recently lost a few percent of their mass should show orbital eccentricities near 0.1, and these should persist because most valley planets have tidal circularisation times longer than a gigayear.
Multi-planet systems with an inner planet being stripped should have their inner pair period ratio widened by roughly 5-10%, with the expansion saturating near a period ratio of about 2.3 as the torus-planet coupling weakens.
The inner members of gap-straddling pairs should be radius-biased high compared to the general sub-Neptune population, matching the Kepler observation that they resemble stripped cores.
The difference between sub-Neptune pairs and super-Earth pairs in period-ratio spacing implies that only a fraction of planets below the radius gap are produced by this stripping channel, so the mechanism is not required to act on every small planet.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Beyond the paper, a testable extension is that the period-ratio shift should scale with the inner-to-outer planet mass ratio $M_1/M_2$, so systems with a heavier inner planet should show more widening; transit-timing mass measurements could look for this.
Beyond the paper, if torus retention is the controlling condition, valley planets around magnetically active stars with strong winds should show lower eccentricities than those around quiet stars, a correlation not yet examined.
Beyond the paper, the angular-momentum transfer should also give the outer member of a gap-straddling pair a modest eccentricity as it absorbs angular momentum from the torus; measuring outer-planet eccentricities would separate this mechanism from pure tidal damping.
Beyond the paper, the model predicts eccentricity excitation confined to the mass-loss episode, so future radial-velocity samples should find elevated eccentricities concentrated near the valley radius rather than spread across all small-planet radii.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

The core idea here is new and worth taking seriously: when a planet loses its envelope, some of the gas can remain as a torus and resonantly extract angular momentum from the planet, pumping eccentricity and, in multi-planet systems, widening period ratios. I have not seen this mechanism in the prior literature, and the paper uses it to explain the Gilbert et al. eccentricity excess in the radius valley. That is a real contribution.

The analytical skeleton is simple and honest. The angular momentum conservation derivations in Section 2 and Appendix A have no free parameters fitted to the target observations; the required envelope mass fractions of a few percent are plausible. The Kepler comparison is a genuine independent test, and the definition of the gap-straddling and comparison samples is clear. The IPP/OPP difference is also an interesting observation in its own right, and the paper is candid that it implies not every below-gap planet is a stripped core.

The soft spots are real but not all equal. The load-bearing assumption is that the stripped gas stays in the system as a torus for many dynamical timescales. Section 2.1 asserts this for “many, possibly most” mass-losing systems, but the cited examples are hot Jupiters with mass-loss rates orders of magnitude above those expected for the super-Earths populating the radius valley. If the gas is removed quickly, the mechanism produces nothing. The paper never quantifies the retention fraction, which directly affects how much of the 2.3-sigma Kepler signal survives.

There is also a numerical inconsistency in Eq. (2). Direct evaluation of Eq. (1) with the stated Hill-sphere aspect ratio gives p ≈ 0.24 for the reference parameters, not 2.465. The threshold p > 0.157 is still passed, so the direction of the argument survives, but the margin is thinner than the text implies and the quoted constant is wrong. The period-ratio expansion in Fig. 5 also requires inner eccentricities near 0.2 to get the 5–10% widening, while the observed eccentricities are closer to 0.1; the secular-sharing argument softens that but does not erase it. The valley strip is calibrated post hoc on the same data, and there is no completeness correction.

Overall, this paper deserves a serious referee. The mechanism is testable, the angular momentum bookkeeping is transparent, and the observational test is a genuine prediction. A referee should focus on the torus retention physics and the numerical consistency of Section 2. I would bring it to reading group and would cite it if I worked on the radius valley.

Referee Report

4 major / 5 minor

Summary. The paper proposes that when a super-Earth loses its gaseous envelope, the stripped gas can remain in the system as a torus exterior to the planet. Lindblad resonances then transfer angular momentum from the planetary orbit to the torus, pumping the planet's eccentricity; in multi-planet systems the same torus can mediate angular-momentum transfer to an outer planet and widen the period ratio. The author derives a parameter-light angular-momentum scaling (e ~ sqrt(f w_f)), estimates that a few percent envelope mass fraction can produce eccentricities of order 0.1, and presents a Kepler-based comparison in which pairs straddling the radius valley have period ratios shifted by roughly 5-10% relative to pairs that both lie above the valley. The paper argues that the observed eccentricity excess near the radius gap and the pair widening are evidence that stripped gas remained in the system long enough to interact gravitationally.

Significance. If the mechanism operates, it provides a physical link between envelope stripping and dynamical excitation, with an explicit and falsifiable prediction: planets in or near the radius valley should have elevated eccentricities, and gap-straddling pairs should be wider. A notable strength is the explicit angular-momentum bookkeeping in Eqs. (4) and (6), which does not fit parameters to the target observations; the Kepler control samples are also a reasonable first test. The significance is presently conditional: the central results all depend on the unquantified persistence of a coherent gas torus, and several technical inconsistencies in the quantitative estimates need correction before the derived magnitudes can be accepted.

major comments (4)

[§2.1, Eq. (2)] Equation (2) does not follow from Eq. (1) with the stated Hill-sphere aspect ratio. For M_p = 10 M_Earth, M_* = M_Sun, e_p = 0.01, and alpha = 0.01, taking h/r = (M_p/(3M_*))^(1/3) gives p ~ 0.24, about an order of magnitude below the quoted 2.465; the quoted coefficient instead corresponds to e_p ~ 0.1 while Eq. (2) is written with e_p/0.01. This is not purely cosmetic, because p then lies only slightly above the p > 0.157 excitation threshold, and the value G(p) = 1.3 used in Eq. (3) is evaluated at p = 2.465. The authors should correct the coefficient or state a different assumed h/r, then recompute G(p) and the eccentricity-growth timescale t_e.
[§2.1] The mechanism requires the stripped envelope to persist as a coherent exterior torus for the angular-momentum exchange timescale, but the statement that "in many, possibly most, of the mass-losing systems, the gas stripped from the planet remains present in the system for many dynamical timescales" is asserted without quantitative support. The cited examples (WASP-12b, GJ436) are hot Jupiters with mass-loss rates orders of magnitude above those expected for the super-Earths that populate the radius valley. If the torus is removed on a dynamical timescale, none of the subsequent predictions follow. The authors should provide at least an order-of-magnitude estimate of torus lifetime for the relevant parameter regime (e.g., against stellar-wind ram pressure, radiation pressure, and magnetic stresses), or explicitly treat the retention fraction as an unknown parameter and propagate it into the predicted GSP/OPP contrast.
[Appendix A, Eqs. (A4)-(A7)] Equation (A4) is inconsistent with the angular-momentum balance written in Eqs. (A1) and (A3): the term representing the initial envelope mass, -f(M1/M2), is missing from the constant term. The expression in Eq. (6) of the main text is the solution of the corrected equation, so the printed A4 appears to be a typographical error. More importantly, Eq. (A7) and the stated minimum e1^2 > 2f(P2/P1)^(1/3) do not follow from the corrected equation; a first-order solution gives a finite-f correction proportional to f(1-x0)/x0^2 with x0 = (P2/P1)^(1/6), which vanishes as x0 approaches unity, rather than the -2f term in A7. This affects the accessible-region curves in Fig. 5 and the inferred mass-loss fractions in Section 4. The authors should re-derive the finite-f expansions and update the affected discussion.
[§4.1, Fig. 3] The empirical support for the pair-widening claim is weaker than the abstract implies. The GSP/OPP difference rests on a KS probability of p = 0.018 (2.3 sigma), and the "5-10%" shift is a visual characterization of the cumulative distributions rather than a fitted quantity. In addition, the radius-valley window was calibrated by moving the strip to identify the most empty gap, so the significance estimate does not account for this data-driven choice. Because the expected shift is diluted if the torus-retention fraction is below unity, the Kepler comparison should be made against a model with a retention fraction rather than a pure shift of the entire distribution.

minor comments (5)

[§2.1, Eq. (3)] The function G(p) is not defined; the authors should give the saturation formula from Goldreich & Sari (2003) or otherwise specify how G(p) is evaluated for values other than p = 2.465.
[§2.2] There is a typographical error in "This will stall ,the outward evolution" and "seperated" should be "separated".
[Figure 2] The core masses in the text are written as "5.5, 8.5 and 13M_sun"; these should be Earth masses (M_Earth) to be consistent with the model context.
[§4.1] The statement that in-gap pairs show a larger shift and imply mass-loss fractions closer to 10% is based on only 13 IGP systems; this should be labeled as tentative.
[Fig. 3 caption] The dotted red histogram (GSP distribution divided by 1.05) is not described in the main text; it would help to point the reader to this comparison explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the eccentricity and period-ratio results are derived from conserved angular momentum with stated physical inputs, and the Kepler comparison is an independent empirical test.

full rationale

The paper's derivation chain is self-contained conditional on its stated assumptions. Equation (3) adapts the published Lindblad-resonance pumping rate (Goldreich & Tremaine 1980; Goldreich & Sari 2003) with explicit inputs f, w, alpha, M_p, M_*, and e_p. Equation (4) is an angular-momentum bookkeeping relation for a planet that loses mass fraction f into an exterior torus that migrates to offset w_f; both f and w_f are stated model inputs, not quantities fitted to the eccentricity or period-ratio data. The Kepler test in Section 4.1 compares the period-ratio distributions of independently defined 'gap-straddling pairs' (GSP) and 'outer pairs-in-a-pod' (OPP); the quoted ~5-10% shift and KS probability p=0.018 are an empirical comparison, and the model parameters are not fit to that sample. The only self-citations appear as contextual planet-incidence statistics (Zink et al. 2019) and a secondary secular-damping remark in Appendix A (Hansen & Murray 2015); neither carries the load of the eccentricity-excitation or period-ratio derivation. The assertion in Section 2.1 that stripped gas 'remains present in the system for many dynamical timescales' is an explicit physical precondition, not a derived consequence, so the concern about torus persistence is a robustness question about an input assumption rather than circularity. No equation or prediction reduces by construction to fitted data or to a self-citation chain.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The model's outputs scale with f and w_f, which are physical inputs rather than fits to the Kepler data. The only fitted parameter in the observational test is the placement of the radius-valley strip. The main unstated physical premises are the persistence and exterior location of the torus and the applicability of disk resonance formulas to a low-mass ring.

free parameters (5)

envelope mass fraction f = 0.01-0.1 (few percent)
Scales the eccentricity (Eq. 4) and pair expansion; chosen from envelope mass fraction estimates, not fitted to the Kepler data.
torque stall offset w_f = ~0.3 a_p (m=5 resonance)
Determines the final eccentricity via Eq. (4); set by the weakening of Lindblad resonances beyond order m=5.
disk viscosity alpha = 0.01
Enters the saturation parameter p (Eq. 2); a standard protoplanetary disk value, not measured for stripped-envelope gas.
tidal quality factor Q_p = 10^3 (rocky), 10^4 (sub-Neptune)
Used in the tidal circularisation threshold (Eq. 5); taken from literature (Banfield & Murray 1992; Ray et al. 2001).
radius valley strip location = 1.81-2.06 R_Earth at P=10 days, slope (P/10d)^-0.11
The strip is calibrated on the Berger et al. (2020) sample to maximize the emptiness of the gap; a fitted nuisance parameter for the GSP/OPP comparison.

assumptions (5)

domain assumption Stripped gas remains as a coherent exterior torus for many dynamical timescales
Stated in §2.1; if stellar winds remove the gas promptly, the torque mechanism does not operate.
domain assumption Protoplanetary disk resonance torque formulae apply to a narrow, low-mass torus
Eq. (3) adapts Goldreich & Tremaine (1980) and Goldreich & Sari (2003); the torus has mass far below a protoplanetary disk and no external mass reservoir.
domain assumption Torus sits exterior to the planet, so outer Lindblad resonances dominate and pump eccentricity
Assumed in §2.1; an interior or co-orbital configuration would change the sign and magnitude of the eccentricity evolution.
ad hoc to paper The torus equilibrium position in a two-planet system is the geometric mean of the planetary semi-major axes (a_t^2 = a1 a2')
Invoked in the Appendix to close the angular-momentum balance; no dynamical derivation is given for this equilibrium.
standard math Keplerian dynamics and angular momentum conservation
Used throughout the derivations in §§2-4 and the Appendix.

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Cite this review

Pith. "Pith review of Generating eccentricity from envelope stripping in the Radius Valley." pith.science (2026). https://pith.science/paper/TIS6WCWQ

@misc{pith2026260804231,
  author       = {Pith},
  title        = {Pith review of: Generating eccentricity from envelope stripping in the Radius Valley},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TIS6WCWQ}},
  note         = {Machine review of arXiv:2608.04231}
}

read the original abstract

We demonstrate that the stripping of planetary envelopes can result in the excitation of planetary orbital eccentricity if the stripped gas remains in the system long enough to interact gravitationally and absorb angular momentum from the planetary orbit. We estimate that envelope mass fractions of a few percent can excite eccentricities of order 0.1 for single planets. This process can potentially explain the elevated eccentricities observed for planets whose radii lie in, or near, the radius valley. In multiple planet systems, the stripped gas can mediate angular momentum exchange between neighbouring planets, causing the separation to expand. Using data from the Kepler satellite, we find that planet pairs, whose members straddle the radius valley, do appear to be systematically wider than those in which both members are sub-Neptunes. These results support the idea that planets in, or just below, the radius valley are the stripped cores of planets that have lost mass, because the elevated eccentricities represent evidence that the gas remained in the system long enough to absorb additional angular momentum from the planet.

Figures

Figures reproduced from arXiv: 2608.04231 by the authors.

**Figure 1.** — The solid contours indicate contours of constant final planetary eccentricity, given the amount of mass lost (f) and the separation to which the ring migrates (wf ). The horizontal dotted lines indicate the locations of first order Outer Lindblad resonances (the density of such resonances increases towards the bottom of the plot and the dense web at the bottom has been omitted for clarity). The error bar on the ri… view at source ↗

**Figure 2.** — The solid points represent planets from the catalog of Berger et al. (2020). The solid curves represent the criterion that τe = 109 years, for two different values of Q=103 (rocky planets) and Q=104 (Neptunes). The transition from one limit to the other, as the envelope evaporates, is uncertain. Therefore, the region between the two estimates represents a region of uncertainty – planets that should be circularised… view at source ↗

**Figure 3.** shows the cumulative distribution of nearest neighbour period ratios for each of these samples. The first thing to notice is the distinct mismatch between the green (IPP) and black (OPP) histograms – the probability that these two samples are drawn from the same distribution is only p = 2 × 10−6 . The fact that these two populations have different spacings suggests that not every planet below the radius gap is simp… view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: — The black histogram, in the left hand panel, shows the cumulative distribution of radii for the members of the OPP sample, while red histogram shows the radius distribution for the outer members of the GSP sample. The blue histogram shows the same for the IGP sample…

**Figure 5.** Figure 5: — The black solid curves show the combination of initial period ratio and final inner eccentricity that result in a period expansion factor of 1.05 (leftmost) or 1.10 (rightmost), assuming the mass in the torus is negligible – assuming an initially equal mass pair. The…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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