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arxiv: 2606.26232 · v1 · pith:CBVKG5KEnew · submitted 2026-06-24 · 🌌 astro-ph.SR · astro-ph.EP

Modeling the curved dust sublimation front in protoplanetary disks: a potential probe of midplane turbulence

Ezequiel Manzo-Mart\'inez (1 , 2) , Ramiro Franco-Hern\'andez (3) , Nuria Calvet (2) , Jes\'us Hern\'andez (1) , Paola D'Alessio (4) , Rosa M. Torres (3) ((1) Instituto de Astronom\'ia-UNAM , (2) University of Michigan
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(3) Universidad de Guadalajara (4) Instituto de Radioastronom\'ia y Astrof\'isica-UNAM)
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Pith reviewed 2026-06-26 01:23 UTC · model grok-4.3

classification 🌌 astro-ph.SR astro-ph.EP
keywords protoplanetary disksdust sublimationT Tauri starsnear-infrared colorsturbulencedust settlingspectral energy distributions
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The pith

Matching observed JHK colors of T Tauri stars requires millimeter grains to reach 0.5-3 scale heights above the midplane.

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

The paper introduces a self-consistent calculation of the curved dust sublimation front in T Tauri disks that uses the disk structure and a density-dependent sublimation temperature to set the wall geometry. Synthetic SEDs are generated for models around a 0.5 solar-mass star, with the wall extending from roughly 0.11 to 0.38 au, and the effects of accretion rate, settling, inclination, and the height of the millimeter-grain layer are tested. Comparison with observed near-IR colors from Taurus, IC 348, and Orion shows that standard parameters cover most of the data, but the densest regions of color space are populated only when large grains extend well above the midplane.

Core claim

The curved dust inner wall starts at about 0.11 au and reaches 0.38 au; reproducing the concentration of observed JHK colors in a large T Tauri sample requires that millimeter-sized grains be distributed up to 0.5-3 scale heights above the midplane, which contradicts rapid settling and points to high midplane turbulence.

What carries the argument

The curved dust inner wall whose radial and vertical extent is fixed self-consistently by the disk density structure and density-dependent sublimation temperature, together with the vertical scale height occupied by the millimeter-grain population.

If this is right

  • T Tauri disks must maintain significant turbulence near the star to keep large grains aloft against settling.
  • Near-IR color diagnostics can constrain the strength of midplane turbulence in the inner disk.
  • SED modeling of the inner wall must incorporate vertically extended large-grain layers to match observations accurately.
  • Rapid dust settling is not occurring in the inner regions sampled by JHK emission.

Where Pith is reading between the lines

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

  • Sustained turbulence in the inner disk could slow the early stages of planetesimal formation by keeping solids suspended.
  • The same modeling approach could be extended to longer wavelengths to test whether grain lifting persists at larger radii.
  • Correlation between required grain heights and independent turbulence tracers such as line widths could be checked with existing data.

Load-bearing premise

The observed JHK colors are produced mainly by emission from the modeled curved wall and the vertical distribution of large grains, rather than other disk regions or unmodeled effects.

What would settle it

Interferometric or scattered-light observations that place millimeter grains below 0.5 scale heights throughout the inner disk would falsify the requirement for extended grain heights.

Figures

Figures reproduced from arXiv: 2606.26232 by 2), (2) University of Michigan, (3) Universidad de Guadalajara, (4) Instituto de Radioastronom\'ia y Astrof\'isica-UNAM), Ezequiel Manzo-Mart\'inez (1, Jes\'us Hern\'andez (1), Nuria Calvet (2), Paola D'Alessio (4), Ramiro Franco-Hern\'andez (3), Rosa M. Torres (3) ((1) Instituto de Astronom\'ia-UNAM.

Figure 1
Figure 1. Figure 1: Color-color diagram in the JHK bands for our CTTSs sample (green points). The shaded blue region is the corresponding normalized two-dimensional KDE map, assuming a Gaussian kernel. to unity over all ([J − H], [H − K]) values. For visual￾ization we mask extremely low-density values (< 10−8 ), and display the map with a linear colormap. For ref￾erence, we overplotted as green points the individual CTTS colo… view at source ↗
Figure 2
Figure 2. Figure 2: Sublimation temperature vs density for olivine from Pollack et al. (1994). 3.3. Wall emission To compute the emission from the curved wall, we first determined the angle between the incident stellar radiation and the normal vector of each surface element of the wall. For this, we fitted a third-degree polynomial to the curved wall geometry (see Section 4.2) and dis￾cretized the surface area into a grid of … view at source ↗
Figure 3
Figure 3. Figure 3: Visualization of the shape of the curved wall model as seen at an inclination cos(i) = 0.4. The parameters are M˙ = 1 × 10−8 M⊙ yr−1 , ϵ = 0.01, and zbig = 0.1 H, for a 0.5 M⊙ star. Note that the lower wall is not visible except through the central hole. The star is shown at the center. 4. RESULTS 4.1. Curved walls for various disk models [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Third-degree polynomial fit to the geometry of the wall (red line) shown in the disk dust density plot (blue region), for various zbig values. The disk parameters are M˙ = 1 × 10−8 M⊙ yr−1 and ϵ = 0.01, for a 0.5 M⊙, 1 Myr old star. The thick black dashed line is the location of a vertical wall with Tsub = 1400 K, while in orange we show the scale height at different values, as indicated by the labels. au … view at source ↗
Figure 5
Figure 5. Figure 5: Third-degree polynomial fit to the geometry of the wall (red solid thick line) shown in the disk temperature structure, for various zbig values. The disk parameters are M˙ = 1 × 10−8 M⊙ yr−1 and ϵ = 0.01, for a 0.5 M⊙, 1 Myr old star. The black line is the location of a vertical wall with Tsub = 1400 K. Dashed lines are temperature isocontours for: 100, 300, 500, 1000, and 1400 K, from right to left. els c… view at source ↗
Figure 6
Figure 6. Figure 6: Physical properties at the wall as a function of the disk height, for a model with zbig = 3H, M˙ = 1 × 10−8M⊙ yr−1 , ϵ = 0.01, and a 0.5 M⊙, 1 Myr star. We show the wall geometry (upper left), the dust and sublimation temperatures (upper right), the disk density (middle left), the abundances of large and small grains (middle right), the total mean opacity (lower left) and the mean true opacity (lower right… view at source ↗
Figure 7
Figure 7. Figure 7: SEDs of the curved wall plus star for various zbig values: 0.5 H (blue), 1 H (orange), 2 H (green), and 3 H (red). The stellar photosphere is shown in black. The disk model has M∗ = 0.5 M⊙ and M˙ = 1 × 10−8M⊙ yr−1 , with cos(i) = 0.5, for ϵ = 0.01 (solid) and ϵ = 0.0001 (dashed). Additional ϵ values within the parameter space de￾scribed above were also considered when comparing the models with the observat… view at source ↗
Figure 8
Figure 8. Figure 8: SEDs of disk models with curved walls. The upper panels are models with ϵ = 0.001, M˙ = 1 × 10−8M⊙ yr−1 , and zbig = 0.5 H. Two inclinations are shown: cos(i) = 0.4 (i = 66.4 o , upper left) and cos(i) = 0.9 (i = 25.8 o , upper right). Both panels show the contribution from the star (yellow), the curved wall (blue), the disk (green), the accretion shocks (magenta), and the total (black). The lower panels s… view at source ↗
Figure 9
Figure 9. Figure 9: KDE maps of the observed dereddened JHK colors (blue region), with relative density isocontours shown at values of 9, 7.5, 6, 4.5, 3, and 1.5, from innermost (highest relative density) to outermost (lowest relative density). The colored symbols correspond to models with curved walls for different cos(i) as indicated by the labels. The first row shows models with ϵ = 0.01 and the second row models with ϵ = … view at source ↗
Figure 10
Figure 10. Figure 10: Distributions of log(ϵ) (upper left), M˙ (upper right), cos(i) (lower left), and zbig (lower right), of the disk models that populate the region defined by the two innermost relative density isocontours (with KDE values 9 and 7.5) of the observations [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Cumulative distributions of log(ϵ) (upper left), M˙ (upper right), cos(i) (lower left), and zbig (lower right), of the disk models that populate the region defined by the two innermost relative density isocontours (with KDE values 9 and 7.5) of the observations [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
read the original abstract

We present a new approach to calculate the geometry and emission of the dust inner wall in disks around T Tauri stars. This calculation follows a self-consistent approach given the disk structure and adopts a density-dependent sublimation temperature for the dust. We built spectral energy distributions (SEDs) of disk models with curved walls around a $0.5\,M_\odot$ star, finding that the curved wall starts at a radius of $\sim 0.11$ au and extends to $\sim 0.38$ au. The dependence on mass accretion rate, dust settling, and disk inclination on the resulting SEDs is explored, as well as the impact of the height of the midplane layer containing large millimeter-sized grains. To test our models, we compare synthetic near-IR colors from a grid of disk models with observed colors for a large sample of disk-bearing T Tauri stars located in Taurus, IC 348, and the Orion complex. Most of the observed colors can be explained by combinations of mass accretion rates, dust settling, and inclinations within the expected ranges for T Tauri stars. However, populating the regions where observed JHK colors are most concentrated, requires the millimeter-size grains be spread up to 0.5--3 scale heights above the midplane. This result contradicts expectations of rapid dust settling and suggests a high degree of turbulence capable of lifting large grains toward the upper disk layers. These findings provide insight into the dynamical conditions of the disk midplane near the 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

3 major / 2 minor

Summary. The paper presents a self-consistent calculation of the curved dust sublimation front in T Tauri protoplanetary disks that incorporates a density-dependent sublimation temperature. For a 0.5 M⊙ star the resulting wall extends from ~0.11 au to ~0.38 au. SEDs are generated while varying mass-accretion rate, dust-settling parameter, inclination, and the vertical height of the millimeter-grain layer; synthetic JHK colors from this grid are then compared with photometry of disk-bearing T Tauri stars in Taurus, IC 348 and Orion. The authors conclude that most observed colors are reproduced by plausible ranges of the first three parameters, but that the densest observed color loci require millimeter grains lifted to 0.5–3 scale heights, implying a high level of midplane turbulence.

Significance. If the central inference holds, the work supplies an observational diagnostic of midplane turbulence near the star that challenges the standard expectation of rapid dust settling. The self-consistent treatment of the sublimation front geometry and temperature is a clear methodological advance over earlier fixed-wall approximations. The comparison across three star-forming regions adds breadth to the parameter study.

major comments (3)
  1. [§4] §4 (color comparison and turbulence conclusion): the claim that millimeter grains must reach 0.5–3 scale heights rests on visual inspection of color-color diagrams without reported quantitative fit statistics (e.g., χ², KS-test p-values, or overlap fractions with error bars). Because the turbulence inference is drawn directly from this comparison, the absence of statistical measures is load-bearing.
  2. [§3] Model assumptions (abstract and §3): the interpretation that the observed JHK colors are dominated by emission from the modeled curved wall plus the vertically extended mm-grain layer is not tested against alternative inner-disk configurations (flat wall, additional hot inner component, or scattering contributions). Without such tests the requirement for elevated grain heights—and therefore turbulence—does not necessarily follow.
  3. [grid description] Parameter exploration (grid description): the four free parameters (accretion rate, settling, inclination, grain height) are varied, yet no degeneracy analysis is presented showing whether combinations of the first three parameters alone can populate the densest observed loci when grain height is held at the canonical settled value.
minor comments (2)
  1. [figures] Figure captions for the color-color plots should explicitly state the number of observed stars plotted and the precise definition of the model grid points shown.
  2. [notation] Notation for the dust-settling parameter and the grain-height parameter should be defined once in the text and used consistently thereafter.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important areas for strengthening the statistical rigor and scope of the analysis. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [§4] §4 (color comparison and turbulence conclusion): the claim that millimeter grains must reach 0.5–3 scale heights rests on visual inspection of color-color diagrams without reported quantitative fit statistics (e.g., χ², KS-test p-values, or overlap fractions with error bars). Because the turbulence inference is drawn directly from this comparison, the absence of statistical measures is load-bearing.

    Authors: We agree that quantitative statistics would make the comparison more rigorous. In the revised manuscript we will add χ² values and fractional overlap metrics (with photometric error bars) between the model grids and the observed color loci in each region. These will be computed both for the full grid and for the subset with canonical settled grain heights, directly quantifying the improvement provided by elevated mm-grain layers. revision: yes

  2. Referee: [§3] Model assumptions (abstract and §3): the interpretation that the observed JHK colors are dominated by emission from the modeled curved wall plus the vertically extended mm-grain layer is not tested against alternative inner-disk configurations (flat wall, additional hot inner component, or scattering contributions). Without such tests the requirement for elevated grain heights—and therefore turbulence—does not necessarily follow.

    Authors: The manuscript is deliberately scoped to the self-consistent curved-wall geometry; we do not claim the result is unique across all possible inner-disk models. We will add a short paragraph in §4 and the conclusions explicitly noting this scope limitation and stating that the turbulence inference applies within the family of curved-wall models. Full exploration of flat-wall or additional-component models lies outside the present study but could be addressed in follow-up work. revision: partial

  3. Referee: [grid description] Parameter exploration (grid description): the four free parameters (accretion rate, settling, inclination, grain height) are varied, yet no degeneracy analysis is presented showing whether combinations of the first three parameters alone can populate the densest observed loci when grain height is held at the canonical settled value.

    Authors: We will include a new subsection (or appendix) that fixes grain height at the settled value (h = 0) and shows the resulting color distribution when accretion rate, settling parameter, and inclination are varied over their full ranges. This will demonstrate that the densest observed loci remain under-populated, thereby confirming that the elevated grain heights are required even after accounting for degeneracies among the other parameters. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central inference drawn from external observational comparison

full rationale

The paper constructs disk models with a density-dependent sublimation temperature to determine the curved inner wall geometry (starting ~0.11 au, extending to ~0.38 au), then varies input parameters (accretion rate, dust settling, inclination, vertical extent of mm-grain layer) to generate synthetic JHK colors. These are compared directly to an external sample of observed colors from Taurus, IC 348, and Orion. The requirement for mm-grains at 0.5-3 scale heights follows from which models populate the densest observed color loci; this step uses the external data as benchmark rather than reducing any quantity to a fitted parameter or self-citation by construction. No load-bearing self-citations, self-definitional steps, or renamed known results are present in the derivation chain. The result is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The central claim rests on several free parameters (accretion rate, dust settling, inclination, and the vertical extent of the mm-grain layer) that are varied to match colors, plus standard domain assumptions about disk vertical structure and radiative transfer; no new entities are postulated.

free parameters (4)
  • mass accretion rate
    Varied across models to explore its effect on the resulting SEDs and colors
  • dust settling parameter
    Explored as a variable controlling how settled the dust is in the models
  • disk inclination
    Varied to assess impact on synthetic near-IR colors
  • height of midplane layer containing large grains
    Adjusted between 0.5-3 scale heights to reproduce the most concentrated observed JHK colors
axioms (2)
  • domain assumption Standard assumptions about the vertical structure and radiative transfer in protoplanetary disks around T Tauri stars
    Used to construct the disk models and compute SEDs
  • domain assumption Density-dependent sublimation temperature for dust
    Adopted as the basis for the self-consistent curved wall geometry

pith-pipeline@v0.9.1-grok · 5899 in / 1801 out tokens · 30485 ms · 2026-06-26T01:23:24.926023+00:00 · methodology

discussion (0)

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