{"id":"e77ea947-f740-4477-8a8f-99e576e199fd","arxiv_id":"2501.04350","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Rotation of lava planets produces a first-order east-west circulation in the supersonic mineral-vapor wind, obtained by perturbing the standard 1D axisymmetric model.","lead":"This paper adds planetary rotation to models of supersonic mineral-vapor winds on lava planets, using a two-dimensional perturbation framework built on an existing one-dimensional solution. It finds that rotation can create a significant east-west circulation that breaks the substellar-to-antistellar symmetry, with implications for observing and interpreting these atmospheres.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The first-order Coriolis expansion is not uniformly small for the target planets: tilde_omega=0.13 and the nightside residuals in Appendix C leave the linear truncation an unvalidated assumption for the broadest applicability claims.","rationale":"The reader correctly identified the perturbative expansion as the weakest assumption, and the paper itself supplies supporting evidence for that concern in Appendix C (residuals comparable on the nightside), Appendix D (nightside instability), and Section 3.3 (solver failure for massive planets). My analysis sharpens the issue: the expansion parameter tilde_omega is based on the sound speed, so the actual Coriolis-to-advection ratio is 2*tilde_omega / tilde_V^(0) and is not small wherever the zeroth-order transport velocity is small. This is a genuine quantitative limitation, but it does not overturn the qualitative mechanism of Coriolis-driven asymmetric circulation; the central claim remains conditionally supported for small tilde_omega. The reader's verdict of CONDITIONAL with moderate confidence is therefore unchanged by this stress-test pass.","tokens_in":17186,"tokens_out":6221,"duration_ms":68499,"concrete_test":"Compute the O(tilde_omega^2) correction to the circulation u in the standard setup, following the method outlined in Section 2.3; if the maximum of the second-order u exceeds roughly 30% of the maximum of the first-order u, or if the second-order terms are not negligible in the region where lambda_22,2D/lambda_22,1D exceeds unity, then first-order truncation is unjustified and the linear rescaling claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the O(tilde_omega) expansion in Eq. 9 and the associated claim (Section 2.3) that the first-order nondimensional solution is universal and can be rescaled by the rotation rate. The expansion parameter is tilde_omega = omega*a / sqrt(Cp*T0), which is 0.13 in the standard run, but the ratio of the Coriolis term to the advection term in Eq. 2 is 2*tilde_omega / tilde_V^(0), which is not uniformly small on the dayside where tilde_V^(0) approaches zero. Appendix C already shows that the residual lambda_22,2D is comparable to the first-order Coriolis term for theta >= 130 degrees, and Appendix D reports instability on the nightside. For typical lava planets the Rossby number is only about 2, and Section 3.3 states that the solver fails for planets more massive than Earth such as K2-141b, so the paper resorts to exponential extrapolation via Eq. 18 and Figure 5. The central mechanism, Coriolis deflection generating an azimuthal flow, is physically plausible, but the linear prediction's quantitative validity in the observationally most relevant regime is not established.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a two-dimensional horizontal model for the mineral-vapor atmospheres of synchronously rotating lava planets. Starting from the axisymmetric one-dimensional solution of Kang et al. (2021), the authors expand the steady primitive equations in the nondimensional rotation rate tilde_omega and solve first-order ODEs (Eq. 12) for the longitude-asymmetric transport and circulation fields, assuming the sinusoidal longitude dependence of Eq. (11). The standard simulation (Mp = 0.05 M_sun, Ts0 = 3200 K, P = 18 h) has tilde_omega = 0.13 and yields asymmetric winds of order several hundred m/s. The paper also maps the sensitivity of first-order amplitudes to a modified mass M* and Ts0, and proposes exponential fits for massive planets where the direct solver fails.","tokens_in":17472,"tokens_out":4160,"duration_ms":44747,"significance":"If the linearized first-order solution is valid, the central claim that planetary rotation generates a substantial azimuthal circulation breaking substellar-point symmetry is physically plausible, and the nondimensional rescaling of the first-order state is a useful design principle for future models. The derivation is transparent and the residual and linear-stability checks in Appendices C and D are a commendable attempt to assess the truncation error. The main weakness is that the paper has not established quantitative validity of the first-order truncation for the nightside and for massive close-in planets such as K2-141b, which are among the most observationally relevant targets. The paper is a promising framework rather than a fully validated prediction.","major_comments":[{"comment":"The perturbation expansion in tilde_omega is the load-bearing step, but the paper's own checks show that it is not uniformly valid. In the standard simulation, the residual λ22,2D becomes comparable to the first-order Coriolis term λ22,1D for θ ≥ 130° (Figure 8), and the linear stability analysis in Appendix D gives positive Re(σ) for θ > 80° (Figure 9). These are exactly the nightside regions where the paper describes convergence west and divergence east of the antistellar point. The authors should either include second-order contributions in the nightside or explicitly restrict the stated validity to θ ≲ 110° and explain why the nightside circulation pattern can still be trusted despite the residual being first-order-comparable.","section":"Section 2.3, Eq. (9)"},{"comment":"The exponential extrapolation Δi = Ai exp(-Bi M*) + Ci is used to estimate first-order amplitudes for planets more massive than Earth, including K2-141b, but the fits are only over M*/M⊕ ≤ 0.25. The manuscript itself states that the solver fails for planets more massive than Earth, and no independent test of the extrapolation is provided. Since K2-141b is a key observational target mentioned in the Introduction, a fitted curve over a limited mass range cannot carry the quantitative applicability claim. Please provide a convergence check or an independent numerical method for the massive-planet regime, or explicitly reframe those results as a tentative conjecture rather than a prediction.","section":"Section 3.3, Eq. (18) and Figure 5"},{"comment":"The assumed sinusoidal longitude dependence is introduced as a prior and is not derived from the first-order equations. While the Coriolis forcing has a cos φ form, the piecewise mass-flux terms in Eq. (6) and the condensation-boundary treatment in Appendix A introduce θ-dependent jumps and define the first-order condensation flux δD through saturation conditions that are not obviously compatible with a single m = 1 harmonic. The nonlinear residual λ1 in Eq. (C16) already contains wave-number-two structure (Figure 7), so the completeness of the m = 1 ansatz at first order should be justified explicitly, or the error from neglected longitude harmonics should be quantified for the first-order state.","section":"Section 2.3, Eq. (11)"}],"minor_comments":[{"comment":"The heading contains a typo: 'Nondimensionlization' should be 'Nondimensionalization'.","section":"Section 2.3 heading"},{"comment":"The table header reads 'T able 1'; this should be corrected to 'Table 1'.","section":"Table 1"},{"comment":"The caption uses 'phi' instead of the mathematical symbol φ; this makes the sentence hard to parse and should be fixed.","section":"Figure 7 caption"},{"comment":"The abstract states that the expansion is with respect to 1/Ro where Ro exceeds unity for typical lava planets, but the expansion parameter in Eq. (9) is defined with the sound speed, not the flow speed. The authors should clarify the relation between tilde_omega and the Rossby number actually used in the lava-planet literature, since the local ratio of Coriolis to advection terms is 2 tilde_omega / tilde_V^(0), which is not uniformly small.","section":"Abstract and Section 3.3"}],"recommendation":"major_revision","confidential_remarks":"The manuscript leans heavily on Kang et al. (2021), including its numerical solution as the zeroth-order state and its parameter choices. This is not circular because the first-order equations use that state as an input, but the dependence on a single prior model makes the sensitivity analysis narrower than it appears. The self-citation pattern is understandable given the direct use of that model, but the authors should consider citing independent 3D or 2D lava-planet circulation studies more broadly. The main editorial question is whether the scope of the claims can be honestly narrowed to small planets and day-side flow; if so, the paper can become a useful contribution after revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the punchline: this is the first paper to add planetary rotation to the 1D supersonic-flow framework for lava planet mineral-vapor atmospheres. It does this by a first-order perturbation expansion in the nondimensional spin parameter, and it works out the asymmetric circulation that results. The mechanism—Coriolis deflection of the transport flow drives an azimuthal circulation that breaks substellar symmetry—is physically sensible and matches the pattern you'd expect from the shallow-water tidally-locked literature.\n\nWhat's genuinely good: the derivation is transparent and mostly self-contained. The authors start from the known 1D axisymmetric solution, linearize the governing equations, and solve a well-posed set of ODEs. The appendices are a real strength. They check the residual of the truncated expansion (Appendix C), test sensitivity to the integration starting point (Appendix B), and attempt a crude linear stability analysis (Appendix D). That's more honesty than most papers in this area show. The approximation for the circulation velocity u1 is also nice: a simple balance between Coriolis acceleration and momentum drag from evaporation, which reproduces the exact solution away from the antistellar point.\n\nNow the soft spots, and they are real but not fatal. The expansion parameter is 0.13 in the standard run, but the relevant Rossby number for typical lava planets is only about 2, so the expansion is not as small as you'd like. The paper's own residual analysis shows the second-order terms are comparable to the first-order Coriolis term on the nightside, and the stability appendix reports growing modes there. That doesn't kill the mechanism, but it means the quantitative solution is only reliable on the dayside and near the terminator. The bigger issue is extrapolation to massive planets like K2-141b. The solver fails there, so the authors fit exponential curves to the low-mass results and extrapolate. They are upfront that this is a hypothesis, but the extrapolated numbers should not be treated as predictions.\n\nThe paper doesn't ship code or data, which is a minor annoyance. The reference list includes several self-citations to Kang et al. (2021), but that's appropriate because the method is built directly on that model.\n\nBottom line: this is a solid, careful first step. The central mechanism is plausible and the framework is reusable. The quantitative claims for the most interesting planets are conditional on better convergence and a proper nonlinear treatment, so the broad applicability statements need to be softened. Send it to peer review; a good referee will push on the expansion validity and the extrapolation, but the core contribution deserves a forum.\n\nWho it's for: exoplanet atmosphere modelers who care about lava planets, and anyone extending 1D condensation-driven flow models to include rotation. Worth engaging with seriously.","headline":"A careful first-order perturbation of the lava-planet flow model shows rotation generates an asymmetric circulation, but the expansion is not uniformly small for the massive close-in planets that are the prime targets.","tokens_in":17975,"tokens_out":2862,"would_cite":true,"duration_ms":27233,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The rotation of a lava planet produces a Coriolis-driven circulation that breaks the substellar-point symmetry assumed by all earlier axisymmetric models, with the first-order asymmetry proportional to the nondimensional spin rate.","keywords":["lava planets","mineral vapor atmosphere","planetary rotation","Coriolis effect","supersonic flow","perturbation expansion","tidally locked","Rossby number"],"falsifier":"Run a nonlinear three-dimensional atmospheric simulation of a lava planet with the standard parameters but with $\\tilde{\\omega}$ near 0.5: if the azimuthal wind and the $m=1$ pressure pattern do not scale approximately linearly with $\\tilde{\\omega}$ and match $u_1, V_1, P_1, T_1$, the perturbation expansion is falsified for realistic spin rates. A cheaper test is to compare the paper's fitted extrapolation for K2-141b with the observed phase curve: the model predicts a specific westward-convergence/eastward-divergence asymmetry, so a phase curve with the opposite longitudinal shift, or with a much larger amplitude than $\\tilde{\\omega}$ times the first-order solution, would rule the claim out.","tokens_in":16970,"feed_emoji":"🌋","tokens_out":7725,"duration_ms":68923,"temperature":0.7,"pith_summary":"This paper extends the standard one-dimensional model of supersonic mineral-vapor flow on lava planets to two horizontal dimensions by treating planetary rotation as a small perturbation. It shows that the Coriolis force deflects the day-to-night supersonic transport into an east-west circulation, so the atmosphere is no longer symmetric about the substellar-antistellar axis. The asymmetric component is the part of the flow that would show up in phase-curve observations, drive magma-ocean currents, and slowly deform the planet's shape, so knowing its structure matters for interpreting lava planets. The paper also maps how the asymmetry depends on planetary mass, density, surface temperature, and the sticking coefficient for surface-atmosphere exchange.","feed_headline":"Lava-planet spin breaks the symmetric supersonic flow","feed_subtitle":"Coriolis deflection creates east-west winds that change how we read phase curves and magma oceans.","key_machinery":"The load-bearing object is the perturbation expansion in $\\tilde{\\omega}$, the ratio of planetary rotation speed to the sound speed scale $\\sqrt{C_p T_0}$, which is the inverse Rossby number built on the sound speed. Because lava-planet winds are supersonic, the expansions of all fields are written as the known 1D axisymmetric solution plus a first-order term, and the azimuthal structure is fixed by the Coriolis force to be first harmonic in longitude: $u_1\\cos\\phi$ for the circulation and $V_1, P_1, T_1$ for transport, pressure, and temperature. Substituting this ansatz reduces the 2D problem to a linear system of four ODEs in the tidally locked latitude $\\theta$, with coefficient matrices constructed entirely from zeroth-order quantities; the sonic-point singularity is handled by a binary search on the boundary condition at the substellar point so that the solution passes smoothly through the critical point.","core_discovery":"Starting from the established axisymmetric solution in which mineral vapor evaporates near the substellar point and accelerates to supersonic speeds toward the nightside, the paper solves the first-order correction to the steady horizontal flow produced by the Coriolis force. Expanding all fields in the nondimensional spin parameter $\\tilde{\\omega} = \\omega a / \\sqrt{C_p T_0}$, it finds that the first-order azimuthal (circulation) velocity takes the form $u^{(1)} = -\\omega a\\,u_1(\\theta)\\cos\\phi$ while the transport, pressure, and temperature corrections vary as $\\sin\\phi$, with the amplitudes determined by a linear system of ODEs whose coefficients depend only on the zeroth-order axisymmetric state. The calculation confirms that rotation generically breaks substellar-point symmetry, producing convergence west of the antistellar point and divergence east of it, and that the nondimensional first-order state is universal for a given zeroth-order state, independent of the actual rotation rate. Relative to the background flow, the asymmetric corrections are largest for small, cool, low-mass lava planets and for weak surface sticking; for the standard simulation the azimuthal circulation reaches hundreds of meters per second.","pith_inferences":["If the paper's exponential fits for the relative asymmetry continue to hold beyond the solved mass range, the asymmetry on a massive planet like K2-141b would be sizable even though the solver fails there; that extrapolation is proposed but not established.","The residual analysis shows wave-number-two terms that are small on the dayside but comparable to the first-order terms beyond $\\theta \\approx 130^\\circ$, so a second-order calculation would likely shift the longitude of maximum pressure and temperature away from the pure $\\sin\\phi$ prediction.","Because the linear stability analysis finds growing modes only on the nightside, where the flow is supersonic and cannot propagate information upstream, the steady dayside solution may be a robust attractor even if the nightside is time-dependent.","The predicted surface wind-stress pattern gives a concrete forcing field for models of lava-ocean currents, offering a testable bridge between this atmospheric result and observed shape or thermal anomalies."],"forward_implications":["The substellar-to-antistellar symmetry assumed by earlier models is broken by rotation; the first-order pattern is a zonal circulation that accelerates with latitude and is strongest away from the substellar point.","Because the nondimensional first-order state depends only on the zeroth-order state, one reference solution can be rescaled to any planetary rotation rate for which $\\tilde{\\omega}$ stays small.","Asymmetric pressure and temperature fields of order $\\tilde{\\omega}$ times the background imply observable signatures in thermal phase curves and in the surface wind stress that drives magma-ocean circulation.","The relative asymmetry is largest for small, cool lava planets and for surfaces with smaller sticking coefficient $\\alpha$, which behaves like a reduced effective mass $M^* \\equiv \\alpha^{3/2}(\\rho_p/\\rho_\\oplus)^{1/2} M_p$.","In the standard simulation the azimuthal circulation $\\omega a u_1$ reaches hundreds of meters per second, meaning rotation cannot be neglected when interpreting the flow."],"supporting_citations":[{"why":"Supplies the 1D axisymmetric mineral-vapor solution and the surface mass-exchange formulation whose zeroth-order state is the starting point of the perturbation.","marker":"Kang et al. 2021"},{"why":"Provided the Rossby-number estimate (about 2) for lava planets and first conjectured that rotation would induce asymmetric flow.","marker":"Castan & Menou 2011"},{"why":"Established the sublimation-driven sonic-point flow regime that the axisymmetric lava-planet solution inherits.","marker":"Ingersoll et al. 1985"},{"why":"Gave the shallow-water picture of rotation breaking substellar symmetry on tidally locked planets that motivates the 2D extension.","marker":"Showman & Polvani 2011"},{"why":"Modeled mineral-vapor outgassing and diffusion barriers, informing the parameterization of surface-atmosphere mass exchange.","marker":"Kite et al. 2016"},{"why":"Provided the non-parallel stellar illumination geometry used to set the surface temperature boundary condition.","marker":"Nguyen et al. 2020"},{"why":"Reported the symmetric, large-amplitude phase curve of K2-141b that motivates the tenuous mineral-vapor scenario and defines the massive-planet limit.","marker":"Zieba et al. 2022"}],"fun_headline_variants":["Lava planet spin twists supersonic winds","Rotation breaks symmetry in lava planet supersonic flows","Coriolis force bends supersonic winds on lava planets","New 2D model: lava planet rotation drives asymmetric winds","Spin creates east-west asymmetry in lava planet atmospheres"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole calculation assumes the spin rate is a small parameter and that the first-order term captures the asymmetry; the paper itself notes that typical lava planets have Rossby number only about 2 and that the solver fails for massive planets like K2-141b, so this small-spin premise is not established for the most observationally interesting cases.","fun_headline_variants_meta":{"raw":{"variants":["Lava planet spin twists supersonic winds","Rotation breaks symmetry in lava planet supersonic flows","Coriolis force bends supersonic winds on lava planets","New 2D model: lava planet rotation drives asymmetric winds","Spin creates east-west asymmetry in lava planet atmospheres"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000219,"raw_usage":{"total_tokens":1478,"prompt_tokens":1017,"completion_tokens":461,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":633,"completion_tokens_details":{"reasoning_tokens":382}},"tokens_in":633,"tokens_out":461,"duration_ms":4650,"temperature":1.0,"reasoning_tokens":382,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:35:43.454042+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a nonlinear three-dimensional atmospheric simulation of a lava planet with the standard parameters but with $\\tilde{\\omega}$ near 0.5: if the azimuthal wind and the $m=1$ pressure pattern do not scale approximately linearly with $\\tilde{\\omega}$ and match $u_1, V_1, P_1, T_1$, the perturbation expansion is falsified for realistic spin rates. A cheaper test is to compare the paper's fitted extrapolation for K2-141b with the observed phase curve: the model predicts a specific westward-convergence/eastward-divergence asymmetry, so a phase curve with the opposite longitudinal shift, or with a much larger amplitude than $\\tilde{\\omega}$ times the first-order solution, would rule the claim out.","supporting_citations":[{"cited_title":"2021, , 906, 67, 10.3847/1538-4357/abcaa7","cited_arxiv_id":null,"evidence_quote":"Supplies the 1D axisymmetric mineral-vapor solution and the surface mass-exchange formulation whose zeroth-order state is the starting point of the perturbation."},{"cited_title":"P., Summers , M","cited_arxiv_id":null,"evidence_quote":"Established the sublimation-driven sonic-point flow regime that the axisymmetric lava-planet solution inherits."}],"review_version":1}