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arxiv: 2603.26204 · v2 · submitted 2026-03-27 · 🌌 astro-ph.EP

The role of inner disk edges in shaping ultra-short-period planet systems around late M dwarfs

S. N. Brandenberger , M. Sanchez , N. Van der Marel , A. A. Vidotto , Y. Miguel This is my paper

Pith reviewed 2026-05-14 23:05 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords ultra-short-period planetslate M dwarfsdisk inner edgepebble accretionplanet migrationN-body simulationsprotoplanetary disks
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The pith

The location of a protoplanetary disk's inner edge determines whether ultra-short-period planets form around late M dwarfs.

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

N-body simulations show that ultra-short-period planets around late M dwarfs form only when the disk inner edge stays close to the star or moves inward with the corotation radius. Planets grow from lunar-mass seeds by pebble accretion and migrate by tracking the edge's position in low-viscosity disks. The fixed close-in edge and inward-evolving edge scenarios produce these planets while an outward-evolving edge does not. This directly ties the survival of planets with periods shorter than one day to how the disk truncates near the star.

Core claim

Ultra-short-period planet formation is tightly controlled by the location of the disk's inner edge. In simulations with planet-disk interactions, star-planet tidal interactions, and relativistic corrections, planets tend to follow the movement of the disk's inner edge. Only the close-in-fixed-edge scenario and the inward-evolving-edge scenario are capable of producing USP planets. This suggests that USP planet formation is favored when the inner edge remains close to the corotation radius of a rapidly rotating star.

What carries the argument

The inner edge of the protoplanetary disk modeled in three prescriptions (fixed close-in, outward-evolving magnetospheric truncation, inward-evolving corotation radius), with planets tracking its location during migration.

Load-bearing premise

The disk has very low viscosity with planets growing from lunar-mass seeds via pebble accretion, and the three specific inner-edge prescriptions accurately represent real disk physics without additional migration barriers.

What would settle it

Detection of an ultra-short-period planet in a system where the disk inner edge is observed to evolve outward would contradict the finding that only close-in or inward-evolving edges produce such planets.

Figures

Figures reproduced from arXiv: 2603.26204 by A. A. Vidotto, M. Sanchez, N. Van der Marel, S. N. Brandenberger, Y. Miguel.

Figure 1
Figure 1. Figure 1: Inner disk edge scenarios cartoons. From left to right: FIX Scenario with close-in fixed inner disk edge; OUT[M] Scenario [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Inner disk edge evolution. Fixed inner edge (FIX; dashed [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Dynamical evolution of planetary embryos in a representative simulation of Scenario FIX. Each line corresponds to one [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average close-encounter events per system for each [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Fraction of initial embryos per system that experienced an [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Final planetary architectures for the three inner-edge pre [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Planetary mass as a function of orbital period for our [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Left: Detection probability map for TESS as a function of orbital period and planetary mass. Colors indicate the probability [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Cumulative distributions of adjacent period ratios. Simu [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Period-ratio distribution of adjacent planet pairs, [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
read the original abstract

Close-in rocky planets are the most common type of exoplanets around late M dwarfs, ranging from more temperate worlds to highly irradiated lava planets with molten surfaces, and many theoretical studies have attempted to explain their formation. However, the origin of rocky planets with orbital periods shorter than one day, known as ultra-short-period (USP) planets, remains uncertain. We aim to investigate whether the formation and survival of USP planets is connected to the location of the inner edge of the protoplanetary disk, considering different disk edge prescriptions. We use N-body simulations that include planet-disk interactions, star-planet tidal interactions, and relativistic corrections, applied to a sample of lunar-mass planetary seeds growing via pebble accretion in a low-viscosity disk ($\alpha_t = 10^{-4}$). The inner edge of the disk is modeled in three ways: as a fixed close-in edge, as an outward-evolving edge set by the magnetospheric truncation radius, and as an inward-evolving edge defined by the corotation radius. USP planet formation appears to be tightly controlled by the location of the disk's inner edge. Our simulations show that only the close-in-fixed-edge Scenario and the inward-evolving-edge Scenario are capable of producing USP planets, as planets tend to follow the movement of the disk's inner edge. This suggests that USP planet formation is favored when the inner edge remains close to the corotation radius of a rapidly rotating star.

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 / 2 minor

Summary. The paper uses N-body simulations of lunar-mass seeds growing by pebble accretion in a disk with fixed α_t=10^{-4} to test three inner-edge prescriptions (fixed close-in, outward-evolving magnetospheric truncation, inward-evolving corotation). It claims that USP planets form only when the inner edge is fixed close-in or evolves inward, because planets follow the edge location, implying that USP formation is tightly controlled by the disk inner edge and favored near the corotation radius of a rapidly rotating star.

Significance. If the central claim holds, the work supplies a concrete dynamical mechanism connecting disk-edge evolution to the observed excess of USP planets around late M dwarfs. The forward-simulation approach from stated initial conditions and torque prescriptions is a strength, as it avoids post-hoc fitting and yields falsifiable predictions for how stellar rotation and disk truncation affect close-in planet populations.

major comments (2)
  1. [Simulation setup] Simulation setup (disk model): All runs fix α_t=10^{-4}. The skeptic correctly notes that higher viscosity alters type-I torque saturation and gap-opening criteria, which could allow planets to decouple from an outward-evolving edge and produce USPs in the third scenario. Without a viscosity sweep or explicit justification that α_t=10^{-4} is the relevant regime for late-M-dwarf disks, the assertion that formation is 'tightly controlled' by edge location rests on an untested assumption and is not general.
  2. [Results] Results section (USP production statistics): The claim that only the close-in-fixed and inward-evolving scenarios produce USPs is presented as robust, yet the manuscript provides no quantitative comparison of final semi-major-axis distributions or migration timescales across the three edge cases at the same initial conditions. A table or figure showing the fraction of seeds reaching P<1 day in each scenario, with error bars from multiple realizations, is needed to substantiate the 'only' qualifier.
minor comments (2)
  1. [Abstract] The abstract states 'planets tend to follow the movement of the disk's inner edge' without defining the quantitative criterion used to identify 'following' (e.g., |a_p - r_edge| < some threshold). This should be stated explicitly in the methods.
  2. [Methods] Clarify whether the three edge prescriptions are mutually exclusive or could coexist in a single disk model; the current framing treats them as separate scenarios without discussing possible transitions between them.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed report. Their comments have prompted us to clarify key aspects of our simulation setup and strengthen the quantitative presentation of our results. We address each major comment below.

read point-by-point responses

  1. Referee: [Simulation setup] Simulation setup (disk model): All runs fix α_t=10^{-4}. The skeptic correctly notes that higher viscosity alters type-I torque saturation and gap-opening criteria, which could allow planets to decouple from an outward-evolving edge and produce USPs in the third scenario. Without a viscosity sweep or explicit justification that α_t=10^{-4} is the relevant regime for late-M-dwarf disks, the assertion that formation is 'tightly controlled' by edge location rests on an untested assumption and is not general.

    Authors: We selected α_t = 10^{-4} to represent the low-viscosity regime characteristic of the inner regions of disks around late M dwarfs, consistent with observational constraints on accretion rates and theoretical models of dead-zone physics in such systems. At this value, lunar-mass seeds remain firmly in the type-I migration regime without gap opening, enabling them to track the inner edge as intended. While a full viscosity parameter study would test broader applicability, the scope of this work is to isolate the dynamical role of the three inner-edge prescriptions under representative conditions. In the revised manuscript we have added an explicit justification paragraph in the Methods section, including references to relevant M-dwarf disk viscosity studies. revision: partial

  2. Referee: [Results] Results section (USP production statistics): The claim that only the close-in-fixed and inward-evolving scenarios produce USPs is presented as robust, yet the manuscript provides no quantitative comparison of final semi-major-axis distributions or migration timescales across the three edge cases at the same initial conditions. A table or figure showing the fraction of seeds reaching P<1 day in each scenario, with error bars from multiple realizations, is needed to substantiate the 'only' qualifier.

    Authors: We agree that a concise quantitative summary improves clarity. Although the original figures display the final semi-major-axis distributions and migration histories for each scenario, we have now added a new table in the Results section. This table reports the fraction of seeds that reach P < 1 day in each of the three edge scenarios, together with uncertainties derived from multiple independent realizations. revision: yes

Circularity Check

0 steps flagged

No circularity: forward N-body results from explicit assumptions

full rationale

The paper reports outcomes of N-body simulations that incorporate planet-disk interactions, star-planet tides, and relativistic corrections applied to lunar-mass seeds growing by pebble accretion in a disk with fixed α_t = 10^{-4}. The claim that only the close-in-fixed-edge and inward-evolving-edge scenarios produce USP planets follows directly from the numerical evolution under the three stated inner-edge prescriptions; it does not reduce by construction to a fitted parameter, a self-citation chain, or any redefinition of inputs. All load-bearing steps are forward modeling from stated physical assumptions and initial conditions rather than any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

Simulations rest on standard assumptions in disk-planet theory plus specific numerical choices for viscosity and seed masses; no new entities postulated.

free parameters (2)
  • alpha_t = 10^{-4}
    Disk viscosity parameter set to 10^{-4} for low-viscosity regime.
  • initial seed mass = lunar mass
    Planetary seeds initialized at lunar mass for pebble accretion growth.
axioms (2)
  • domain assumption N-body integration accurately captures planet-disk interactions, tidal forces, and relativistic corrections.
    Invoked for all simulation runs as standard modeling approach.
  • domain assumption Pebble accretion is the dominant growth mechanism in the low-viscosity disk.
    Used to evolve lunar-mass seeds into planets.

pith-pipeline@v0.9.0 · 5578 in / 1448 out tokens · 40028 ms · 2026-05-14T23:05:08.803031+00:00 · methodology

discussion (0)

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