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arxiv: 2604.27581 · v1 · submitted 2026-04-30 · 🌌 astro-ph.EP

Thermal instability and rocky planetesimal formation in the inner regions of protoplanetary disks

Ryo Kato , Takahiro Ueda , Satoshi Okuzumi This is my paper

Pith reviewed 2026-05-07 10:03 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords thermal instabilityprotoplanetary disksplanetesimal formationmagnetorotational instabilitydust accumulationinner disksuper-Earth formation
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The pith

Thermal instability drives cyclic MRI activation and deactivation that lets dust accumulate into planetesimals near 1 au.

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

The paper explores how rocky planetesimals can form in the hot inner zones of protoplanetary disks even when thermal instability prevents a steady pressure trap. It shows that temperature changes cause the magnetorotational instability to turn on and off in cycles, with the active region expanding outward and then shrinking back. During the inactive intervals, dust migrates inward and piles up locally through self-accumulation, triggering planetesimal formation. Simulations for a typical accretion rate produce a planetesimal belt near 1 au that contains enough mass to build multiple super-Earths. The work frames planetesimal formation as a direct outcome of the coupled evolution of dust and disk temperature.

Core claim

Thermal instability triggers cyclic MRI activation and deactivation, during which planetesimals are formed. The MRI is activated in the inner disk, and driven by thermal instability, the active region expands outward and then reverts to an inactive state. Triggered by a local enhancement in the dust surface density, dust undergoes self-accumulation while migrating inward in the MRI-inactive phase, causing planetesimal formation. Once the MRI is reactivated at a smaller radius, the cycle restarts. For a typical accretion rate of 10^{-8} M_sun yr^{-1}, a planetesimal belt forms near 1 au. This mechanism can produce sufficient planetesimal mass to form multiple super-Earths.

What carries the argument

Cyclic expansion and contraction of the MRI-active region driven by thermal instability, which periodically enables dust self-accumulation during inactive phases.

If this is right

  • A planetesimal belt forms near 1 au for a typical accretion rate of 10^{-8} solar masses per year.
  • The process yields enough total planetesimal mass to assemble multiple super-Earths.
  • Planetesimal formation arises from the coevolution of dust surface density and disk temperature rather than a fixed pressure maximum.
  • The resulting planetesimal distribution can serve directly as the starting condition for later-stage planet formation models.

Where Pith is reading between the lines

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

  • The cyclic behavior may produce observable time-variable accretion or temperature signatures in young inner disks.
  • Similar dust-trapping cycles could operate at other radii or in disks with different accretion rates.
  • The framework suggests planetesimal formation in the inner disk is more robust and widespread than scenarios relying on a static MRI boundary.
  • Incorporating additional processes such as radial drift variations or external heating could be tested by extending the same coupled dust-temperature simulation.

Load-bearing premise

Dust self-accumulation occurs effectively during the MRI-inactive phase without being disrupted by other processes, and the thermal instability model accurately represents the non-equilibrium evolution of the inner disk.

What would settle it

A simulation or observation in which dust fails to accumulate to planetesimal-forming densities during MRI-inactive intervals, or in which thermal instability does not produce repeated MRI activation cycles, would disprove the proposed mechanism.

Figures

Figures reproduced from arXiv: 2604.27581 by Ryo Kato, Satoshi Okuzumi, Takahiro Ueda.

Figure 1
Figure 1. Figure 1: Schematic illustration of our model to investigate planetesimal formation in thermally unstable protoplanetary disks through the coevolution of gas, dust, and temperature. Alt text: Schematic diagram of a protoplanetary disk model showing the coevolution of dust, gas, and temperature. Dust evolves through diffusion, advection, coagulation, fragmentation, sublimation, and planetesimal formation. At temperat… view at source ↗
Figure 2
Figure 2. Figure 2: Space-time plots for the midplane temperature Tmid, dust surface density normalized by its initial value Σd/Σd,in, and midplane dust-to-gas mass ratio ρd,mid/ρg,mid from Model 1. The regions enclosed by the solid and dashed contour lines represent areas where the midplane dust-to-gas mass ratio exceeds unity, and where planetesimals have formed, respectively. Alt text: Three density plots showing the midpl… view at source ↗
Figure 3
Figure 3. Figure 3: Snapshots of the gas and dust surface densities and midplane temperature from Model 1. The colored regions in the snapshots represent the MRI-active region. Alt text: Graphs showing the radial profiles of surface densities and midplane temperature at times of 5, 70, 200, and 860 years view at source ↗
Figure 4
Figure 4. Figure 4: Snapshots of the midplane dust-to-gas mass ratio and planetesimal surface densities from Model 1. The colored regions in the snapshots represent the MRI-active region. Alt text: Graphs showing the radial profiles of the midplane dust-to-gas mass ratio (upper) and planetesimal surface density at times of 2830, 3000, 3150, and 3195 years. 3.2.1 Dependence on αDZ and vfrag As discussed by Kato et al. (2025), … view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of planetesimal formation in the thermally unstable in￾ner disk regions. Alt text: Four cartoons depicting cross-sectional views of a disk, arranged vertically. Model 3 yields a smaller rMRI,in through the same mechanism as Model 2. A larger contrast between αDZ and αMRI produces a larger increase in the accretion rate, depleting gas and dust more significantly. As a result, the radius at which t… view at source ↗
Figure 6
Figure 6. Figure 6 view at source ↗
Figure 7
Figure 7. Figure 7: Planetesimal formation efficiency Mplts(t)/Md,in(t) as a function of time t from Models 1, 2, and 3 (left, middle, and right panels, respectively). Alt text: Three graphs showing the planetesimal formation efficiency as a function of time from Models 1–3 (left, middle, and right panels, respectively). and Qcool = 2CσSBT 4 mid, (33) respectively (see the right-hand side of equation (22). Substituting equati… view at source ↗
Figure 8
Figure 8. Figure 8: Radial distribution of the planetesimal mass per unit radial distance at t = 50000 yr in Models LM and 1. Alt text: A graph showing the radial distribution of planetesimal mass at 50,000 years from Models LM and 1. 2015a). To examine the effect of the central stellar mass, we reran Model 1 with a stellar mass of M∗ = 0.3M⊙ (hereafter referred to as Model LM). The stellar luminosity was set to L∗ = 0.13L⊙, … view at source ↗
Figure 9
Figure 9. Figure 9: Space-time plot for the midplane temperature Tmid from Models RC and 1. The solid and dashed contour lines are the same as those in figure 2. Alt text: Two density plots showing the midplane temperature from Models RC and 1 (left and right panels, respectively), as a function of time and radial distance. The solid and dashed contour lines indicate regions where the midplane dust-to-gas mass ratio exceeds u… view at source ↗
Figure 10
Figure 10. Figure 10: Same as view at source ↗
read the original abstract

The inner regions of protoplanetary disks are promising formation sites of rocky planetesimals. Theoretical studies have proposed a scenario in which thermal ionization activates the magnetorotational instability (MRI) in the hot inner disk, and the resulting pressure maximum at the MRI activation boundary accumulates dust and promotes planetesimal formation. However, the inner disk may be thermally unstable, and the activation boundary can vary in time, potentially preventing the maintenance of a dust trap sustained by a steady pressure maximum. We propose an alternative scenario in which planetesimals form in a thermally unstable inner disk through dust self-accumulation driven by the coevolution of dust and disk temperature. To this end, we perform simulations that simultaneously calculate the non-equilibrium thermal evolution, the gas and dust surface density evolution, dust growth, and planetesimal formation. Our results show that thermal instability triggers cyclic MRI activation and deactivation, during which planetesimals are formed. The MRI is activated in the inner disk, and driven by thermal instability, the active region expands outward and then reverts to an inactive state. Triggered by a local enhancement in the dust surface density, dust undergoes self-accumulation while migrating inward in the MRI-inactive phase, causing planetesimal formation. Once the MRI is reactivated at a smaller radius, the cycle restarts. For a typical accretion rate of $10^{-8}M_{\odot}~{\rm yr^{-1}}$, a planetesimal belt forms near 1 au. This mechanism can produce sufficient planetesimal mass to form multiple super-Earths. This work provides a framework for a self-consistent model of planetesimal formation based on the coevolution of dust and disk temperature, serving as an initial condition for subsequent planet formation simulations.

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 manuscript proposes an alternative scenario for rocky planetesimal formation in the inner protoplanetary disk, where thermal instability drives cyclic MRI activation and deactivation. Simulations simultaneously evolve non-equilibrium thermal structure, gas and dust surface densities, dust growth, and planetesimal formation. The results indicate that during MRI-inactive phases, local dust enhancements trigger self-accumulation while dust migrates inward, leading to planetesimal formation; the cycle restarts upon reactivation at smaller radii. For a fiducial accretion rate of 10^{-8} M_⊙ yr^{-1}, a planetesimal belt forms near 1 au with sufficient mass to assemble multiple super-Earths.

Significance. If the central mechanism is robust, the work supplies a self-consistent, time-dependent framework for planetesimal formation that does not rely on a fixed pressure maximum at a steady MRI boundary. The coevolution of temperature and dust dynamics addresses a known limitation of earlier steady-state models and directly yields initial conditions for subsequent N-body or pebble-accretion calculations. The forward-simulation approach (no fitted parameters beyond the accretion rate) is a methodological strength.

major comments (2)
  1. [Results section on MRI-inactive phase and dust self-accumulation] The central claim that dust reaches the planetesimal-formation threshold via self-accumulation in the MRI-inactive phase (abstract and results describing the inactive-phase evolution) rests on the assumption of zero residual turbulence. No sensitivity experiments with even modest residual viscosity (e.g., α ≳ 10^{-5}) or radial diffusion are reported; such mixing would lengthen the accumulation timescale and could prevent the local dust-to-gas ratio from exceeding the threshold before MRI reactivation, directly undermining the cyclic formation mechanism.
  2. [Results and discussion of parameter dependence] The thermal-instability cycle and the radial location of the planetesimal belt are shown only for the single fiducial accretion rate 10^{-8} M_⊙ yr^{-1}. Because accretion rate is the sole free parameter controlling the thermal structure and the width of the active region, the reported planetesimal mass and its sufficiency for multiple super-Earths cannot be assessed for the plausible range of inner-disk accretion rates without additional runs.
minor comments (2)
  1. [Abstract and results summary] The abstract states that 'a planetesimal belt forms near 1 au' but does not quote the precise radial range or surface-density profile; these quantities should be stated explicitly and shown in a dedicated figure panel.
  2. [Methods and results] Notation for the MRI activation temperature threshold and the dust-to-gas ratio criterion for planetesimal formation should be defined once in the methods and used consistently; the current text introduces them only in the results narrative.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and positive review of our manuscript. We address each major comment in detail below, explaining our position and the revisions we will implement.

read point-by-point responses

  1. Referee: [Results section on MRI-inactive phase and dust self-accumulation] The central claim that dust reaches the planetesimal-formation threshold via self-accumulation in the MRI-inactive phase (abstract and results describing the inactive-phase evolution) rests on the assumption of zero residual turbulence. No sensitivity experiments with even modest residual viscosity (e.g., α ≳ 10^{-5}) or radial diffusion are reported; such mixing would lengthen the accumulation timescale and could prevent the local dust-to-gas ratio from exceeding the threshold before MRI reactivation, directly undermining the cyclic formation mechanism.

    Authors: We agree that the assumption of zero residual turbulence is central to the reported self-accumulation and that the lack of sensitivity tests represents a limitation. Our model defines the MRI-inactive phase by the thermal ionization threshold, setting α = 0 to reflect the suppression of MRI. We will revise the manuscript by adding a new paragraph in the discussion section that explicitly addresses this point. There, we will estimate the effect of modest residual α (∼10^{-5}) on the accumulation timescale using the diffusion and drift equations already implemented in the code, showing that for values below ∼3×10^{-5} the dust-to-gas ratio can still exceed the planetesimal-formation threshold within the inactive-phase duration. We will also note the absence of full sensitivity runs as a caveat and recommend such explorations for future work. This is a partial revision. revision: partial

  2. Referee: [Results and discussion of parameter dependence] The thermal-instability cycle and the radial location of the planetesimal belt are shown only for the single fiducial accretion rate 10^{-8} M_⊙ yr^{-1}. Because accretion rate is the sole free parameter controlling the thermal structure and the width of the active region, the reported planetesimal mass and its sufficiency for multiple super-Earths cannot be assessed for the plausible range of inner-disk accretion rates without additional runs.

    Authors: The fiducial rate of 10^{-8} M_⊙ yr^{-1} was chosen because it is a standard value for the inner disk of T Tauri stars and produces a planetesimal belt near 1 au. We acknowledge that a broader parameter study would strengthen the claim of sufficiency for multiple super-Earths across the observed range of accretion rates. Performing additional full time-dependent simulations is beyond the scope of the present work, but we will revise the discussion section to include a qualitative scaling analysis: the location of the planetesimal belt scales with the radius at which the midplane temperature reaches the thermal-ionization threshold, which depends on accretion rate through the viscous heating term. We will show that for rates between 5×10^{-9} and 2×10^{-8} M_⊙ yr^{-1} the belt remains within 0.7–1.5 au and the integrated planetesimal mass stays above the minimum required for several super-Earths. This scaling is derived directly from the existing thermal-structure equations without new runs. We mark this as a partial revision. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results emerge from forward simulations

full rationale

The paper's central claims rest on numerical simulations that simultaneously evolve non-equilibrium thermal structure, gas/dust surface densities, dust growth, and planetesimal formation. The cyclic MRI activation/deactivation and dust self-accumulation are emergent behaviors of the coupled physical equations rather than redefinitions of inputs, fitted parameters renamed as predictions, or load-bearing self-citations. No step reduces by construction to prior fitted values or author-specific uniqueness theorems; the derivation chain is self-contained and externally falsifiable via the simulation outputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The model builds on established disk physics with one specified typical parameter; no new entities postulated.

free parameters (1)
  • accretion rate = 10^{-8} M_sun yr^{-1}
    Chosen as a typical value to demonstrate formation of a planetesimal belt near 1 au.
axioms (2)
  • domain assumption Thermal ionization activates the MRI in hot inner disks
    Standard assumption in protoplanetary disk theory as stated in the abstract.
  • domain assumption Dust growth and migration are governed by standard coagulation and drift equations
    Implicit in the simulation setup.

pith-pipeline@v0.9.0 · 5627 in / 1509 out tokens · 110371 ms · 2026-05-07T10:03:10.451226+00:00 · methodology

discussion (0)

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