{"id":"17ab6e26-4b10-48b0-810d-88258816d821","arxiv_id":"2608.04231","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Envelope-stripping gas can act as a resonant torus that excites planetary eccentricity and widens multi-planet spacings, offering a dynamical explanation for the elevated eccentricities and widened pairs seen across the Kepler radius valley.","lead":"A new model proposes that the gas stripped from a planet's atmosphere can linger in orbit and pump up the planet's orbital eccentricity. The same gas can push neighboring planets apart, which matches the spacing of planet pairs straddling the radius valley in Kepler data.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Torus persistence is asserted, not demonstrated; all downstream signals depend on it.","rationale":"After reviewing the manuscript, I find the reader's weakest-assumption analysis correct. The core mechanism requires the stripped envelope to remain as an exterior, coherent gas torus for many dynamical timescales. The paper's only support is Section 2.1's assertion that this holds 'in many, possibly most' mass-losing systems, plus analogies to hot Jupiters and simulations of strong-outflow systems. No estimate is made for super-Earths in the radius valley, whose photoevaporative outflows are weaker and whose host stars may have winds that clear the torus. Every result (eccentricity excitation via Lindblad resonances, period-ratio widening, the Kepler GSP/OPP offset) is downstream of this assumption, making it the single most load-bearing point. The angular-momentum bookkeeping in Section 2.2 and Appendix A is internally consistent given a persistent torus; Equations (4) and (A7) follow correctly from conservation laws. The factor-of-ten discrepancy between Equations (1) and (2) in the saturation parameter is real: using the stated Hill-sphere aspect ratio gives p=0.237 rather than 2.465 for the canonical parameters, but it does not flip the sign of the excitation criterion if p_crit=0.157 is taken at face value, so it affects quantitative timescales rather than the existence of the mechanism. The data analysis's post hoc valley calibration and lack of completeness corrections are additional concerns, but they are secondary to the physical precondition of torus persistence. The proposed simulation check would directly test this precondition. Thus the reader's CONDITIONAL verdict stands without change.","tokens_in":13489,"tokens_out":21798,"duration_ms":191942,"concrete_test":"Run a 3D radiation-hydrodynamic simulation of a 10 Earth-mass super-Earth at 0.1 AU undergoing XUV-driven envelope mass loss, with stellar-wind mass-loss rates spanning log(Mdot_w / M_sun/yr) from -14 to -10 and XUV fluxes from 10 to 1000 erg/s/cm^2, and measure the fraction of stripped envelope mass that remains bound in an exterior torus for more than 10^4 yr. If that fraction exceeds 50% across most of parameter space, the assumption holds; if it is below 10%, the mechanism's predicted signals are too diluted to match the observed 2.3sigma period-ratio shift.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.1 states 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,' but no quantitative support or system fraction is provided. The cited examples (WASP-12b, GJ436) are hot Jupiters with mass-loss rates orders of magnitude above those expected for the super-Earths populating the radius valley. For the mechanism to produce the claimed eccentricities e~0.1 and the period-ratio widening of 5-10%, the exterior torus must persist for at least the angular-momentum exchange timescale (~10^4 yr per Section 2.1) against stellar-wind ram pressure, radiation pressure, and magnetic effects. If the torus is removed on a dynamical timescale, the Lindblad torques vanish and both the single-planet eccentricity excitation and the multi-planet period-ratio widening fail. The Kepler comparison is only 2.3sigma (p=0.018); if the torus-retention fraction is significantly below unity, the GSP/OPP difference would be diluted below the claimed signal. This is a missing physical input rather than a numerical detail.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":13743,"tokens_out":20441,"duration_ms":167487,"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":[{"comment":"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.","section":"§2.1, Eq. (2)"},{"comment":"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.","section":"§2.1"},{"comment":"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.","section":"Appendix A, Eqs. (A4)-(A7)"},{"comment":"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.","section":"§4.1, Fig. 3"}],"minor_comments":[{"comment":"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.","section":"§2.1, Eq. (3)"},{"comment":"There is a typographical error in \"This will stall ,the outward evolution\" and \"seperated\" should be \"separated\".","section":"§2.2"},{"comment":"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.","section":"Figure 2"},{"comment":"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.","section":"§4.1"},{"comment":"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.","section":"Fig. 3 caption"}],"recommendation":"major_revision","confidential_remarks":"The central idea is attractive, and the angular-momentum bookkeeping is mostly transparent and parameter-light. However, the unsupported torus persistence, the numerical error in Eq. (2), and the inconsistencies in the Appendix need to be fixed before publication. I would not reject on the statistical weakness alone, but the abstract should be moderated if the Kepler test remains at only 2.3 sigma."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nThe 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.\n\nThere 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.\n\nOverall, 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.","headline":"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.","tokens_in":14226,"tokens_out":3010,"would_cite":true,"duration_ms":27528,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["radius valley","eccentricity excitation","envelope stripping","Lindblad resonances","gaseous torus","Kepler multi-planet systems","period ratio","photoevaporation"],"falsifier":"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.","tokens_in":13269,"feed_emoji":"🪐","tokens_out":8580,"duration_ms":69437,"temperature":0.7,"pith_summary":"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.","feed_headline":"Stripped envelopes pump planet eccentricities to 0.1","feed_subtitle":"A leftover gas torus also widens gap-straddling planet pairs, linking the Kepler radius valley to stripped cores.","key_machinery":"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 $P'_2/P_1 \\sim (P_2/P_1)\\,[1 + (3/2)(M_1/M_2)\\, e_1^2/(P_2/P_1)^{1/3}]$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the observed eccentricity excess for planets in the 1.75-1.93 R⊕ range that this mechanism explains.","marker":"Gilbert et al. 2025"},{"why":"Foundation for wave-launching torques and angular momentum exchange between a planet and a gaseous disk.","marker":"Goldreich & Tremaine 1980"},{"why":"Gives the saturation criterion and eccentricity-pumping timescale that the paper adapts to the stripped-envelope torus.","marker":"Goldreich & Sari 2003"},{"why":"Provides the corotation-resonance saturation parameter p that controls whether Lindblad resonances excite or damp eccentricity.","marker":"Ogilvie & Lubow 2003"},{"why":"Establishes that weak stellar winds produce a long-lived torus while strong winds produce a cometary tail, setting the geometric condition for the mechanism.","marker":"McCann et al. 2019"},{"why":"Defines the radius gap whose stripped-core interpretation the model supports.","marker":"Fulton et al. 2017"},{"why":"Supplies the GAIA-calibrated Kepler radii and the planet sample used for both the period-radius diagram and the pair statistics.","marker":"Berger et al. 2020"},{"why":"Provides the peas-in-a-pod assumption that pairs initially similar in composition, used to argue gap-straddling systems started as outer-pair-like systems.","marker":"Weiss et al. 2018"},{"why":"Gives the tidal circularisation timescale used to argue most valley planets retain excited eccentricities.","marker":"Jackson et al. 2008"}],"fun_headline_variants":["Envelope stripping excites planet orbits to e=0.1","Stripped gas torus widens pairs straddling the radius valley","Envelope loss excites eccentricity and widens planet pairs","How envelope stripping links eccentric planets to the radius valley"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Envelope stripping excites planet orbits to e=0.1","Stripped gas torus widens pairs straddling the radius valley","Envelope loss excites eccentricity and widens planet pairs","How envelope stripping links eccentric planets to the radius valley"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000837,"raw_usage":{"total_tokens":3636,"prompt_tokens":920,"completion_tokens":2716,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":536,"completion_tokens_details":{"reasoning_tokens":2656}},"tokens_in":536,"tokens_out":2716,"duration_ms":17897,"temperature":1.0,"reasoning_tokens":2656,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:42:07.309421+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}