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arxiv: 2604.18682 · v1 · submitted 2026-04-20 · 🌌 astro-ph.EP

Recognition: unknown

Coupled orbital and interior structure evolution of lava planets

Mahesh Herath , Nicolas B. Cowan , Charles-\'Edouard Boukar\'e , Mathieu Dumberry
Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:28 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords lava planetstidal migrationorbital evolutionmagma oceansrocky exoplanetsultra-short-period planetsthermal-orbital coupling
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The pith

Lava planets can reach their tight orbits by migrating inward in two tidal stages tied to mantle melting.

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

The paper builds a numerical model that connects a rocky planet's interior thermal state to the rate at which its orbit shrinks under stellar tides. Mantle melting, driven by both tidal heating and starlight, alters the mantle's response to tides, which in turn controls how fast the orbit decays, producing a feedback loop. The simulations reveal that inward migration from the inner edge of the protoplanetary disk happens in two phases: a fast high-eccentricity phase that halves the orbital distance, followed by a slower low-eccentricity phase that shrinks it by another factor of five. This full journey to periods under one day succeeds only when the planet begins with eccentricity at least 0.9 and experiences continued forcing that keeps eccentricity above 0.01. The same model reproduces the orbits of five out of seven observed lava planets but fails for the remaining two, indicating that not every lava planet followed an identical path.

Core claim

We introduce a coupled thermal-orbital evolution model to explore how rocky planets migrate from the inner edge of the protoplanetary disk, with periods of 1-10 days, to orbital periods of less than a day. In our model, mantle melting is controlled by tidal heating and stellar flux, while orbits evolve via tidal migration. The mantle's tidal quality factor varies with its temperature and structure, creating a feedback loop between thermal evolution and orbital decay. We use our numerical model to simulate the migration of seven known lava planets. Migration occurs in two stages: an initial high-eccentricity stage reducing the semi-major axis by a factor of ∼2, followed by a low-eccentricity

What carries the argument

Coupled thermal-orbital evolution model in which the mantle's tidal quality factor changes with temperature and melting state to create feedback between interior evolution and orbital decay.

If this is right

  • Migration proceeds slowly while the mantle is mostly molten and faster once it becomes mostly solid.
  • Sustained eccentricity forcing above 0.01 is required throughout the second stage to complete the full inward journey.
  • Five of the seven simulated lava planets can reach their present orbits via this pathway; TOI-431b and GJ 367b cannot.
  • The final orbital distance depends on when the mantle solidifies and how the tidal quality factor responds to that change.

Where Pith is reading between the lines

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

  • The same feedback may operate in other close-in rocky planets that are not currently molten, leaving detectable signatures in their current eccentricities or spin states.
  • Atmospheric observations of lava planets could test for chemical imprints left by the high tidal heating that occurred during the first migration stage.
  • If additional planets are found at periods of a few days with moderate eccentricities, they may represent objects that began the second migration stage but have not yet completed it.

Load-bearing premise

The mantle's tidal quality factor varies with temperature and melting state in a specific way that generates the required feedback between thermal state and migration rate.

What would settle it

A direct measurement or simulation showing that a mantle's tidal response does not slow migration when mostly molten and accelerate it when mostly solid, or that no combination of initial eccentricity 0.9 and sustained forcing can shrink an orbit from 0.1 AU to the observed periods of the modeled planets.

Figures

Figures reproduced from arXiv: 2604.18682 by Charles-\'Edouard Boukar\'e, Mahesh Herath, Mathieu Dumberry, Nicolas B. Cowan.

Figure 1
Figure 1. Figure 1: Schematic of the 1D cross section and thermal evolution model from M. Herath et al. (2024). frad is the radiated flux, fmo the heat flux from the magma ocean, fmu the heat flux from the magma mush, fsol is the flux from solid mantle, and fcore the flux from the core. qliquid, qmush and qsolid are the tidal dissipation in the liquid, mush and solid, respectively. Tl, Tm, and Tso denote the temperatures at t… view at source ↗
Figure 2
Figure 2. Figure 2: The tidal quality factor Qp as a function of bulk mantle viscosity based on an Andrade rheology model for the lava planet K2-141b at an orbital frequency of 6.7 hours and a mantle with a thickness of approximately 0.6R⊕. The solid line shows how Qp varies with viscosity for a uniform molten mantle. We did not have any simulated data points to include viscosities below 107 Pa s wherein the viscosity at that… view at source ↗
Figure 3
Figure 3. Figure 3: Migration scenarios for K2-141b starting from semi-major axes of 0.09 and 0.04 AU and initial eccentricities between 0.7 and 0.96. The plots show tests at emin = 10−2 . Each coloured line represents a different final outcome for the simulation. The light green line shows a simulation where the planet did not reach the present orbit of the planet after 10 Gyrs. The dark green line shows a planet that reache… view at source ↗
Figure 4
Figure 4. Figure 4: Outcomes of orbital migration simulations for K2-141b for a variety of initial orbital parameters and min￾imum eccentricities of 10−1 , 10−2 and 10−3 . The colours match those used in [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Outcomes of orbital migration simulations for planets TOI-141b (first row), K2-360b (second row), HD-3167b (third row) and TOI-431b (fourth row), for emin = 10−1 (left column) and emin = 10−2 (right column). The black broken vertical line denotes the current observed location for each planet. The results show that for e0 ≥ 0.9, with emin ≥ 10−2 , we obtain successful migration scenarios for most, but not a… view at source ↗
Figure 6
Figure 6. Figure 6: Orbital and interior evolution of K2-141b for a minimum eccentricity of emin = 10−2 and two different sets of initial conditions that leads to a successful migration of the planet to its current orbit: a0 = 0.09 AU and e0 = 0.96 (left column), a0 = 0.05 AU and e0 = 0.9 (right column). We show the time evolution of: e (panels a, b); a (panels c, d); tidal dissipation and instellation (panels e, f); tidal qu… view at source ↗
Figure 7
Figure 7. Figure 7: The night-side surface temperatures for differ￾ent minimum eccentricities for K2-141b, at its present day orbit. The three lines in blue, green and indigo represent three types of mantle mixtures where the global quality fac￾tor Qp for each was calculated following the method outlined in Section 2.1. The x-axis gives a spread of possible mini￾mum eccentricities at the current orbit. The y-axis gives the re… view at source ↗
read the original abstract

Lava planets likely did not form in their current orbits, instead migrating inward via orbital decay, which influenced the evolution of their magma oceans. We introduce a coupled thermal-orbital evolution model to explore how rocky planets migrate from the inner edge of the protoplanetary disk, with periods of 1-10 days, to orbital periods of less than a day. In our model, mantle melting is controlled by tidal heating and stellar flux, while orbits evolve via tidal migration. The mantle's tidal quality factor varies with its temperature and structure, creating a feedback loop between thermal evolution and orbital decay. We use our numerical model to simulate the migration of seven known lava planets: K2-141b, K2-360b, TOI-141b, TOI-431b, TOI-2431b, HD 3167b and GJ 367b. Migration occurs in two stages: an initial high-eccentricity stage reducing the semi-major axis by a factor of $\sim 2$, followed by a low-eccentricity stage reducing it by a factor of $\sim 5$. A successful migration from $\sim 0.1$ AU to a present-day orbit requires starting eccentricities $\ge 0.9$ and sustained eccentricity forcing with $e_{\mathrm{min}} \ge 10^{-2}$. The rate of migration depends on the state of the mantle: slow when mostly molten, fast when mostly solid. This pathway works for most lava planets, but not for TOI-431b or GJ-367b, suggesting that multiple migration pathways are possible for lava 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

2 major / 3 minor

Summary. The manuscript introduces a numerical model coupling the thermal evolution of lava-planet mantles (melting driven by tidal heating plus stellar insolation) to orbital migration via tidal torques. A temperature- and melt-fraction-dependent tidal quality factor Q creates a feedback loop that modulates migration rate. Simulations for seven observed lava planets (K2-141b, K2-360b, TOI-141b, TOI-431b, TOI-2431b, HD 3167b, GJ 367b) show migration in two stages: an early high-eccentricity phase that reduces semi-major axis by a factor of ~2, followed by a low-eccentricity phase reducing it by ~5. Successful migration from ~0.1 AU requires initial eccentricities ≥0.9 together with sustained forcing at e_min ≥ 10^{-2}. The pathway accounts for most but not all targets, implying multiple migration channels.

Significance. If robust, the work supplies a physically grounded mechanism linking inward migration of ultra-short-period rocky planets to the thermal state of their magma oceans. The coupled treatment is a genuine strength: migration speed emerges naturally from the interior state (slow when largely molten, fast when largely solid) rather than being imposed. The multi-planet application yields concrete, falsifiable predictions. However, because the headline quantitative results (distinct stages, specific reduction factors, eccentricity thresholds) are generated by the particular functional form adopted for Q(T, melt fraction), the significance is currently that such a feedback is possible rather than that it dominates observed systems.

major comments (2)
  1. [Model section] Model section (description of Q(T, φ)): The functional dependence of the tidal quality factor on temperature and melt fraction is introduced without independent calibration against laboratory rheology data, seismic constraints, or other published mantle models. Because this specific form directly produces the two-stage migration behavior and the reported semi-major-axis reduction factors of ~2 and ~5, the central claims are load-bearing on an unvalidated parametrization. A sensitivity study replacing the adopted Q(T, φ) with alternative functional forms (or with constant-Q runs) is required to test whether the two-stage structure survives.
  2. [Results section] Results section (eccentricity thresholds): The statements that migration succeeds only for e_init ≥ 0.9 and sustained e_min ≥ 10^{-2} are presented without a systematic exploration of the joint parameter space or propagation of uncertainties in other inputs (initial mantle temperature, viscosity, core size). These thresholds are load-bearing for the conclusion that the pathway works for most but not all lava planets; the manuscript must quantify how variations in the remaining free parameters shift the required eccentricity bounds.
minor comments (3)
  1. [Abstract] Abstract: the phrase 'periods of 1-10 days' is ambiguous (initial versus final orbits); the text should state the initial semi-major-axis range explicitly.
  2. [Throughout] Throughout: standard tidal evolution equations (da/dt, de/dt) should be accompanied by explicit citations to the precise formulations adopted (e.g., constant-time-lag or constant-phase-lag models).
  3. [Figures] Figures showing orbital evolution: panels would be clearer if they also display the time series of Q or melt fraction to make the feedback loop visually explicit.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive report and for recognizing the value of the coupled thermal-orbital treatment. We address each major comment below and will revise the manuscript to incorporate the requested analyses.

read point-by-point responses

  1. Referee: [Model section] Model section (description of Q(T, φ)): The functional dependence of the tidal quality factor on temperature and melt fraction is introduced without independent calibration against laboratory rheology data, seismic constraints, or other published mantle models. Because this specific form directly produces the two-stage migration behavior and the reported semi-major-axis reduction factors of ~2 and ~5, the central claims are load-bearing on an unvalidated parametrization. A sensitivity study replacing the adopted Q(T, φ) with alternative functional forms (or with constant-Q runs) is required to test whether the two-stage structure survives.

    Authors: We agree that the specific Q(T, φ) parametrization drives the reported two-stage migration and reduction factors. The form was selected to capture the expected drop in dissipation efficiency as the mantle transitions from solid to high-melt-fraction states, consistent with standard rheological models, but we did not perform independent calibration against new laboratory or seismic data. In the revised manuscript we will add a dedicated sensitivity subsection that repeats the full suite of simulations using (i) a constant-Q model and (ii) two alternative temperature- and melt-dependent forms drawn from the literature (an exponential Arrhenius-like dependence and a power-law melt-fraction scaling). These runs will demonstrate whether the two-stage structure and the factor-of-2 / factor-of-5 reductions persist under different Q assumptions. revision: yes

  2. Referee: [Results section] Results section (eccentricity thresholds): The statements that migration succeeds only for e_init ≥ 0.9 and sustained e_min ≥ 10^{-2} are presented without a systematic exploration of the joint parameter space or propagation of uncertainties in other inputs (initial mantle temperature, viscosity, core size). These thresholds are load-bearing for the conclusion that the pathway works for most but not all lava planets; the manuscript must quantify how variations in the remaining free parameters shift the required eccentricity bounds.

    Authors: The eccentricity thresholds are indeed central to the claim that the mechanism operates for most but not all targets. The current results are based on a single set of interior parameters. In the revision we will expand the results section with a systematic parameter study: we will vary initial mantle temperature, reference viscosity, and core radius over observationally motivated ranges, rerun the migration tracks, and tabulate the resulting shifts in the minimum e_init and sustained e_min required for successful migration from ~0.1 AU. Where computationally feasible we will also indicate the sensitivity of the thresholds to these parameters, thereby quantifying the robustness of the “most but not all” conclusion. revision: yes

Circularity Check

0 steps flagged

No circularity: two-stage migration and eccentricity thresholds emerge from forward integration of coupled equations

full rationale

The paper defines a numerical model in which mantle tidal quality factor Q is made to depend on temperature and melt fraction, then integrates the standard tidal evolution equations forward in time for given initial conditions. The reported two-stage migration (a reduced by ~2 then ~5), the requirement e_init >= 0.9, and the e_min >= 10^{-2} threshold are direct outputs of those integrations under the chosen Q(T) parametrization. No parameter is fitted to the final orbital states of the target planets, no self-citation supplies a uniqueness theorem that forces the functional form, and the headline numbers are not algebraically identical to the input assumptions. The model is therefore self-contained; its predictions can be falsified by changing the Q(T) relation or by external constraints on initial eccentricity.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard exoplanet dynamics and rheology assumptions plus specific numerical choices for eccentricity forcing and mantle response; no new entities are postulated.

free parameters (2)
  • initial eccentricity
    Set to >=0.9 to enable successful migration from 0.1 AU; chosen to match the required orbital decay.
  • minimum sustained eccentricity
    Set to >=10^{-2} for the low-eccentricity stage; required to complete the second phase of migration.
axioms (2)
  • domain assumption Orbital decay is driven by tidal migration
    Standard assumption in exoplanet orbital evolution invoked throughout the model description.
  • domain assumption Mantle tidal quality factor depends on temperature and structure
    Core assumption creating the thermal-orbital feedback loop, stated in the abstract.

pith-pipeline@v0.9.0 · 5607 in / 1496 out tokens · 58885 ms · 2026-05-10T03:28:28.942875+00:00 · methodology

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