pith. sign in

arxiv: 2606.23815 · v1 · pith:VGHSFFLMnew · submitted 2026-06-22 · 🌌 astro-ph.EP

Interpreting the scattering surface in protoplanetary disks

Massimiliano Bolchini , Giovanni Rosotti , Marion Villenave , Antonio Garufi , Myriam Benisty , Tilman Birnstiel , Stefano Facchini , Leonardo Testi This is my paper

Pith reviewed 2026-06-26 06:55 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords protoplanetary disksscattered lightscattering surfacedust massgrain growthradiative transferoptical depth
0
0 comments X

The pith

Scattering surface heights in protoplanetary disks can be used to measure the mass contained in small dust grains.

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

The paper builds a semi-analytical model that starts from the path of stellar light through the disk and shows how the height where most scattering occurs depends on the total mass of small grains, the temperature structure, and the dust opacity. The model is checked against full radiative-transfer calculations and then applied to existing scattered-light images of ten disks. It returns global small-dust mass fractions of order one part in a thousand. These fractions line up with the outcome of standard grain-growth calculations once the largest grains have grown to at least 0.1 mm and the size distribution follows a power-law index between three and 3.5. The central result is that scattering-surface data, once the temperature profile is known, give a practical route to the small-grain reservoir that is otherwise hard to isolate.

Core claim

The scattering surface coincides with the layer where the line-of-sight optical depth from the star reaches order unity. A semi-analytical expression for that height, derived from radiative-transfer principles and validated with MCFOST, is applied to measured surface heights. The resulting small-dust mass fractions are of order 10^{-3}. Using standard opacity tables, these fractions are shown to be consistent with modest grain growth (a_max ≳ 0.1 mm) and grain-size distribution indices of 3 to 3.5. The thermal structure exerts the dominant influence on height; dust settling and anisotropic scattering contribute only minor corrections.

What carries the argument

A semi-analytical expression for scattering-surface height obtained by setting the integrated optical depth along the stellar radiation path to order unity, written as a function of total small-dust mass, temperature profile, and dust opacity.

If this is right

  • The thermal structure of the disk strongly controls the observed scattering height.
  • Dust settling and anisotropic scattering produce only small changes in surface height.
  • Ten observed disks return global small-dust mass fractions of order 10^{-3}.
  • These fractions correspond to maximum grain sizes above 0.1 mm and size-distribution power-law indices between 3 and 3.5.

Where Pith is reading between the lines

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

  • Repeated scattering-height measurements on the same disk over several years could track how the small-grain reservoir changes as the disk evolves.
  • Pairing scattering heights with millimeter continuum maps of the same object would allow separate constraints on the small-grain and large-grain populations.
  • The method implicitly assumes the disk is close to hydrostatic equilibrium; significant deviations from that equilibrium would shift the inferred masses.

Load-bearing premise

The temperature structure of the disk is known independently with enough precision that its uncertainty does not dominate the uncertainty assigned to the small-dust mass.

What would settle it

An independent determination of the small-dust mass in any one of the ten disks, obtained for example from detailed modeling of the spectral energy distribution, that differs from the scattering-height value by more than the combined model and observational uncertainties.

Figures

Figures reproduced from arXiv: 2606.23815 by Antonio Garufi, Giovanni Rosotti, Leonardo Testi, Marion Villenave, Massimiliano Bolchini, Myriam Benisty, Stefano Facchini, Tilman Birnstiel.

Figure 1
Figure 1. Figure 1: Model of the path of a ray through the disk. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Differential intensity as a function of z/H for r = 150 AU. Next, we address what sets the scattering surface. At a fixed radius, it is possible to analyze how different contributions to the optical path vary with height, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Contributions to the differential intensity as a function of z in the disk at fixed radius r = 150 AU. Left: Optical depth τ1 and τ2 as a function of z/H. Middle: Attenuation factors e −τ1 and e −τ2 as a function of z/H. Right: Scattering cross-section, σν, as a function of z/H. of the dust in protoplanetary disks is set by the balance between gravity, which pulls the grains towards the mid-plane, and tur￾… view at source ↗
Figure 4
Figure 4. Figure 4: Scattering height at r = 100 AU for different α parameters in the isothermal and non isothermal case, taking dust settling into account. ρs = 1.67 g/cm3 . The results are shown in [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Comparison between the scattering surface from our [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Top: Difference in height between the scattering surface computed in the single scattering approximation or accounting for multiple scattering, at 200 AU. Bottom: Optical depth from the scattering point to the observer as a function of disk’s incli￾nation. 12, we obtain κMsd(R) = (2π) 3/2 rc (1 − e −R/rc ) p kb (µmHGM∗) −1/2 · · Z s0 0 √ Tmid(r) T(z,r)r 5/2 e −r/rc e − µmHGM∗ kb R z 0 z ′dz′ (r 2+z ′2) 3/2… view at source ↗
Figure 7
Figure 7. Figure 7: Top: Measured scattering surfaces from the literature. Middle: Small dust masses as a function of radius inferred from the inverse problem in our work. Bottom: Small dust mass frac￾tion for all the disks in the sample [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Constraints on the maximum grain size and power-law [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Constraints on the maximum grain size and power-law [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

In recent years, extreme adaptive optics have enabled high-resolution, high-contrast scattered-light observations of protoplanetary disks. Interpreting these observations requires an understanding of the scattering surface, which is shaped by the distribution of small dust grains and determines how disks appear in scattered light. We aim to exploit measurements of the scattering surface height to directly constrain the masses of small dust grains in disks. Starting from radiative transfer principles, we developed a semi-analytical model of the stellar radiation path and its interaction with the disk, deriving the height of the scattering surface as a function of disk parameters such as mass, temperature, and opacity. We validated our predictions against the radiative transfer code MCFOST. Using measured scattering heights, we inferred the mass of dust in small grains and the particle size distribution for a sample of ten disks. We confirm previous results indicating that the scattering surface coincides with the region where the integrated optical depth along the stellar path is of order unity. The thermal structure of the disk significantly affects the surface height, while dust settling and anisotropic scattering have comparatively minor effects. Applying our model to observations, we measure global small-dust mass fractions of order (10^{-3}). Using dust-opacity models, we show that these values are consistent with modest grain growth ((a_{\rm max} \gtrsim 0.1,{\rm mm})) and grain-size distribution power-law indices of approximately 3--3.5, as commonly predicted by grain-growth models. Scattering-surface measurements, together with constraints on the disk thermal structure, provide a powerful method for determining the small-dust content of protoplanetary disks.

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 develops a semi-analytical radiative-transfer model for the height of the scattering surface in protoplanetary disks (where the line-of-sight optical depth to the star reaches order unity), validates the model against MCFOST Monte-Carlo calculations, and applies the relation to measured scattering heights in ten disks to infer global small-dust mass fractions of order 10^{-3}. These fractions are shown to be consistent with modest grain growth (a_max ≳ 0.1 mm) and size-distribution indices p ≈ 3–3.5 when standard dust-opacity models are adopted. The work emphasizes that thermal structure dominates the surface height while settling and anisotropic scattering are secondary.

Significance. If the thermal-structure uncertainty can be controlled, the approach supplies a direct, observationally accessible route to the small-grain mass reservoir that complements SED and millimeter continuum methods. The external validation against MCFOST and the application to a multi-disk sample are concrete strengths that increase the utility of scattering-surface measurements for grain-growth studies.

major comments (2)
  1. [Application to observations] Application to the ten-disk sample (final section): the inversion for small-dust surface density inherits the full uncertainty in the adopted T(r,z) profile, yet the manuscript provides no quantitative sensitivity analysis to plausible variations in the midplane-to-surface temperature gradient. Because the abstract itself states that thermal structure significantly affects surface height, a 20–30 % shift in the gradient maps directly into comparable or larger shifts in the reported 10^{-3} mass fractions and the derived a_max and p values; this must be demonstrated before the numerical conclusions can be considered robust.
  2. [Validation and inference] §3 (validation) and the inference step: while the model is validated against MCFOST for fixed parameters, the paper does not show that the same MCFOST runs recover the input small-dust mass when the thermal structure is allowed to vary within the range used for the observational sample. Without this cross-check, it remains unclear whether the semi-analytic inversion remains unbiased once realistic temperature uncertainties are folded in.
minor comments (2)
  1. [Dust-opacity models] Notation for the power-law index of the grain-size distribution is introduced as p but occasionally appears as q in the opacity-model discussion; a single symbol should be used consistently.
  2. [Figure 4] Figure captions for the MCFOST comparison panels should explicitly state the fixed values of a_max and p adopted in each run so that readers can reproduce the test cases.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important aspects of uncertainty quantification that we will address in revision. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Application to observations] Application to the ten-disk sample (final section): the inversion for small-dust surface density inherits the full uncertainty in the adopted T(r,z) profile, yet the manuscript provides no quantitative sensitivity analysis to plausible variations in the midplane-to-surface temperature gradient. Because the abstract itself states that thermal structure significantly affects surface height, a 20–30 % shift in the gradient maps directly into comparable or larger shifts in the reported 10^{-3} mass fractions and the derived a_max and p values; this must be demonstrated before the numerical conclusions can be considered robust.

    Authors: We agree that the lack of a quantitative sensitivity analysis to the adopted temperature gradient is a limitation. In the revised manuscript we will add a dedicated subsection (or appendix) that perturbs the midplane-to-surface temperature gradient by ±20–30 % around the fiducial profiles used for the ten-disk sample, recomputes the inferred small-dust mass fractions, and reports the resulting ranges together with the nominal values. This will directly quantify the propagation of thermal-structure uncertainty into the reported 10^{-3} fractions and the derived grain-growth parameters. revision: yes

  2. Referee: [Validation and inference] §3 (validation) and the inference step: while the model is validated against MCFOST for fixed parameters, the paper does not show that the same MCFOST runs recover the input small-dust mass when the thermal structure is allowed to vary within the range used for the observational sample. Without this cross-check, it remains unclear whether the semi-analytic inversion remains unbiased once realistic temperature uncertainties are folded in.

    Authors: We acknowledge that the MCFOST validation in §3 was performed at fixed thermal structures. To close this gap we will carry out a new set of MCFOST runs in which the temperature profile is varied within the same range adopted for the observational sample, apply the semi-analytic inversion to the resulting synthetic scattering surfaces, and verify that the input small-dust masses are recovered without significant systematic bias. These additional tests and the corresponding figures will be included in the revised §3. revision: yes

Circularity Check

0 steps flagged

Derivation from first-principles radiative transfer is self-contained with external validation

full rationale

The paper derives the scattering-surface height model directly from radiative-transfer principles (optical-depth integral reaching order unity), validates the semi-analytical expressions against the independent MCFOST Monte-Carlo code, and then inverts measured heights for small-dust mass using separate opacity tables. No equation reduces to a fitted parameter renamed as a prediction, no load-bearing premise rests on self-citation, and no ansatz is smuggled via prior work by the same authors. The reported 10^{-3} mass fractions therefore follow from the external height measurements and the independently constrained thermal structure rather than from any definitional equivalence within the paper itself.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The model rests on standard radiative-transfer assumptions plus external inputs for temperature and opacity; no new entities are postulated. Free parameters are limited to those already present in dust-opacity tables and temperature profiles.

free parameters (2)
  • disk temperature structure
    Abstract states thermal structure significantly affects surface height; treated as an input that must be known independently.
  • dust opacity model parameters (a_max, power-law index)
    Used post hoc to interpret the inferred 10^{-3} mass fractions as consistent with grain growth.
axioms (2)
  • domain assumption Scattering surface coincides with region where integrated optical depth along stellar path is of order unity
    Confirmed by the model but treated as a starting point from radiative transfer.
  • domain assumption MCFOST provides an accurate numerical benchmark for the semi-analytical model
    Validation step assumes the Monte-Carlo code is correct.

pith-pipeline@v0.9.1-grok · 5852 in / 1595 out tokens · 23739 ms · 2026-06-26T06:55:52.077134+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

85 extracted references · 81 canonical work pages · 37 internal anchors

  1. [1]

    , keywords =

    Dust opacities for protostellar cores. , keywords =

  2. [2]

    Accretion Disks around Young Objects. II. Tests of Well-mixed Models with ISM Dust. , keywords =. doi:10.1086/308103 , archivePrefix =. astro-ph/9907330 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/308103

  3. [3]

    , year = 1974, month = sep, volume =

    The evolution of viscous discs and the origin of the nebular variables. , year = 1974, month = sep, volume =. doi:10.1093/mnras/168.3.603 , adsurl =

    work page doi:10.1093/mnras/168.3.603 1974

  4. [4]

    arXiv e-prints , keywords =

    Measuring the Two-Dimensional Thermal Structures of Protoplanetary Disks. arXiv e-prints , keywords =. doi:10.48550/arXiv.2509.15196 , archivePrefix =. 2509.15196 , primaryClass =

    work page doi:10.48550/arxiv.2509.15196

  5. [5]

    , keywords =

    The two-dimensional pressure structure of the HD 163296 protoplanetary disk as probed by multi-molecule kinematics. , keywords =. doi:10.1051/0004-6361/202451307 , archivePrefix =. 2501.05517 , primaryClass =

    work page doi:10.1051/0004-6361/202451307

  6. [6]

    , keywords =

    The efficiency of dust trapping in ringed protoplanetary discs. , keywords =. doi:10.1093/mnras/staa1170 , archivePrefix =. 2004.11394 , primaryClass =

    work page doi:10.1093/mnras/staa1170 2004

  7. [7]

    Physical model and observational evidence in MAPS disks

    Rotation curves in protoplanetary disks with thermal stratification. Physical model and observational evidence in MAPS disks. , keywords =. doi:10.1051/0004-6361/202348546 , archivePrefix =. 2402.12236 , primaryClass =

    work page doi:10.1051/0004-6361/202348546

  8. [8]

    Direct mapping of the temperature and velocity gradients in discs. Imaging the vertical CO snow line around IM Lupi

    Direct mapping of the temperature and velocity gradients in discs. Imaging the vertical CO snow line around IM Lupi. , keywords =. doi:10.1051/0004-6361/201731377 , archivePrefix =. 1710.06450 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201731377

  9. [9]

    Molecules with ALMA at Planet-forming Scales (MAPS). IV. Emission Surfaces and Vertical Distribution of Molecules. , keywords =. doi:10.3847/1538-4365/ac1439 , archivePrefix =. 2109.06217 , primaryClass =

    work page doi:10.3847/1538-4365/ac1439

  10. [10]

    , keywords =

    CO Line Emission Surfaces and Vertical Structure in Midinclination Protoplanetary Disks. , keywords =. doi:10.3847/1538-4357/ac6c02 , archivePrefix =. 2205.01776 , primaryClass =

    work page doi:10.3847/1538-4357/ac6c02

  11. [11]

    , keywords =

    Mapping Protoplanetary Disk Vertical Structure with CO Isotopologue Line Emission. , keywords =. doi:10.3847/1538-4357/acb3c4 , archivePrefix =. 2212.08667 , primaryClass =

    work page doi:10.3847/1538-4357/acb3c4

  12. [12]

    , keywords =

    Mapping the Vertical Gas Structure of the Planet-hosting PDS 70 Disk. , keywords =. doi:10.3847/1538-4357/ad24d2 , archivePrefix =. 2401.03018 , primaryClass =

    work page doi:10.3847/1538-4357/ad24d2

  13. [13]

    exoALMA. V. Gaseous Emission Surfaces and Temperature Structures. , keywords =. doi:10.3847/2041-8213/adc437 , archivePrefix =. 2504.19902 , primaryClass =

    work page doi:10.3847/2041-8213/adc437 2041

  14. [14]

    , keywords =

    Dust Growth and Evolution in Protoplanetary Disks. , keywords =. doi:10.1146/annurev-astro-071221-052705 , archivePrefix =. 2312.13287 , primaryClass =

    work page doi:10.1146/annurev-astro-071221-052705

  15. [15]

    , year = 1941, month = jan, volume =

    Diffuse radiation in the Galaxy. , year = 1941, month = jan, volume =. doi:10.1086/144246 , adsurl =

    work page doi:10.1086/144246 1941

  16. [16]

    The effect of dust settling on the appearance of protoplanetary disks

    The effect of dust settling on the appearance of protoplanetary disks. , keywords =. doi:10.1051/0004-6361:20040284 , archivePrefix =. astro-ph/0405226 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:20040284

  17. [17]

    Physical Review , year = 1924, month = jun, volume =

    On the Resistance Experienced by Spheres in their Motion through Gases. Physical Review , year = 1924, month = jun, volume =. doi:10.1103/PhysRev.23.710 , adsurl =

    work page doi:10.1103/physrev.23.710 1924

  18. [18]

    Observations of edge-on protoplanetary disks with ALMA. I. Results from continuum data. , keywords =. doi:10.1051/0004-6361/202038087 , archivePrefix =. 2008.06518 , primaryClass =

    work page doi:10.1051/0004-6361/202038087 2008

  19. [19]

    Observational appearance

    Black holes in binary systems. Observational appearance. , year = 1973, month = jan, volume =

    1973

  20. [20]

    Monte Carlo radiative transfer in protoplanetary disks

    Monte Carlo radiative transfer in protoplanetary disks. , keywords =. doi:10.1051/0004-6361:20053275 , archivePrefix =. astro-ph/0606550 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361:20053275

  21. [21]

    Benchmark problems for continuum radiative transfer. High optical depths, anisotropic scattering, and polarisation

    Benchmark problems for continuum radiative transfer. High optical depths, anisotropic scattering, and polarisation. , keywords =. doi:10.1051/0004-6361/200811555 , archivePrefix =. 0903.1231 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/200811555

  22. [22]

    T., Lee H

    Optical Properties of Interstellar Graphite and Silicate Grains. , keywords =. doi:10.1086/162480 , adsurl =

    work page doi:10.1086/162480

  23. [23]

    From Stardust to Planetesimals , year = 1997, editor =

    Composition and Size of Interstellar Dust. From Stardust to Planetesimals , year = 1997, editor =

    1997

  24. [24]

    Disks around T Tauri Stars with SPHERE (DARTTS-S). I. SPHERE/IRDIS Polarimetric Imaging of Eight Prominent T Tauri Disks. , keywords =. doi:10.3847/1538-4357/aab846 , archivePrefix =. 1803.10882 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/aab846

  25. [25]

    , keywords =

    Observed Polarized Scattered Light Phase Functions of Planet-forming Disks. , keywords =. doi:10.3847/1538-4357/acdc97 , archivePrefix =. 2301.04617 , primaryClass =

    work page doi:10.3847/1538-4357/acdc97

  26. [26]

    , keywords =

    Possible single-armed spiral in the protoplanetary disk around HD 34282. , keywords =. doi:10.1051/0004-6361/201936787 , archivePrefix =. 2010.12202 , primaryClass =

    work page doi:10.1051/0004-6361/201936787 2010

  27. [27]

    Direct detection of scattered light gaps in the transitional disk around HD 97048 with VLT/SPHERE

    Direct detection of scattered light gaps in the transitional disk around HD 97048 with VLT/SPHERE. , keywords =. doi:10.1051/0004-6361/201629265 , archivePrefix =. 1609.04027 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201629265

  28. [28]

    , keywords =

    Composition and Radiative Properties of Grains in Molecular Clouds and Accretion Disks. , keywords =. doi:10.1086/173677 , adsurl =

    work page doi:10.1086/173677

  29. [29]

    Multiwavelength optical properties of compact dust aggregates in protoplanetary disks

    Multiwavelength optical properties of compact dust aggregates in protoplanetary disks. , keywords =. doi:10.1051/0004-6361/201526048 , archivePrefix =. 1510.05426 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201526048

  30. [30]

    Millimeter-wave polarization of protoplanetary disks due to dust scattering

    Millimeter-wave Polarization of Protoplanetary Disks due to Dust Scattering. , keywords =. doi:10.1088/0004-637X/809/1/78 , archivePrefix =. 1504.04812 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/809/1/78

  31. [31]

    ISO spectroscopy of circumstellar dust in the Herbig Ae systems AB Aur and HD 163296

    ISO spectroscopy of circumstellar dust in the Herbig Ae systems AB Aur and HD 163296. , keywords =. doi:10.48550/arXiv.astro-ph/0002440 , archivePrefix =. astro-ph/0002440 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.astro-ph/0002440

  32. [32]

    , keywords =

    Measuring Turbulent Motion in Planet-forming Disks with ALMA: A Detection around DM Tau and Nondetections around MWC 480 and V4046 Sgr. , keywords =. doi:10.3847/1538-4357/ab8cc5 , archivePrefix =. 2004.12176 , primaryClass =

    work page doi:10.3847/1538-4357/ab8cc5 2004

  33. [33]

    Spatial segregation of dust grains in transition disks. SPHERE observations of 2MASS J16083070-3828268 and RXJ1852.3-3700

    Spatial segregation of dust grains in transition disks. SPHERE observations of 2MASS J16083070-3828268 and RXJ1852.3-3700. , keywords =. doi:10.1051/0004-6361/201834800 , archivePrefix =. 1902.04612 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201834800 1902

  34. [34]

    The full census of planet-forming disks with GTO and DESTINYS programs

    The SPHERE view of the Chamaeleon I star-forming region. The full census of planet-forming disks with GTO and DESTINYS programs. , keywords =. doi:10.1051/0004-6361/202244005 , archivePrefix =. 2403.02149 , primaryClass =

    work page doi:10.1051/0004-6361/202244005

  35. [35]

    Molecules with ALMA at Planet-forming Scales (MAPS). XVIII. Kinematic Substructures in the Disks of HD 163296 and MWC 480. , keywords =. doi:10.3847/1538-4365/ac1438 , archivePrefix =. 2109.06218 , primaryClass =

    work page doi:10.3847/1538-4365/ac1438

  36. [36]

    exoALMA. XII. Weighing and Sizing exoALMA Disks with Rotation Curve Modelling. , keywords =. doi:10.3847/2041-8213/adc431 , adsurl =

    work page doi:10.3847/2041-8213/adc431 2041

  37. [37]

    Molecules with ALMA at Planet-forming Scales (MAPS). XIV. Revealing Disk Substructures in Multiwavelength Continuum Emission. , keywords =. doi:10.3847/1538-4365/ac1431 , archivePrefix =. 2109.06433 , primaryClass =

    work page doi:10.3847/1538-4365/ac1431

  38. [38]

    , year = 1996, month = oct, volume =

    Steady-State Size Distribution for the Self-Similar Collision Cascade. , year = 1996, month = oct, volume =. doi:10.1006/icar.1996.0170 , adsurl =

    work page doi:10.1006/icar.1996.0170 1996

  39. [39]

    , keywords =

    Size Distribution of Collisionally Evolved Asteroidal Populations: Analytical Solution for Self-Similar Collision Cascades. , keywords =. doi:10.1006/icar.1994.1010 , adsurl =

    work page doi:10.1006/icar.1994.1010 1994

  40. [40]

    A simple model for the evolution of the dust population in protoplanetary disks

    A simple model for the evolution of the dust population in protoplanetary disks. , keywords =. doi:10.1051/0004-6361/201118136 , archivePrefix =. 1201.5781 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201118136

  41. [41]

    Dust Evolution Can Produce Scattered Light Gaps in Protoplanetary Disks

    Dust Evolution Can Produce Scattered Light Gaps in Protoplanetary Disks. , keywords =. doi:10.1088/2041-8205/813/1/L14 , archivePrefix =. 1510.05660 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/2041-8205/813/1/l14 2041

  42. [42]

    , keywords =

    Constraining the turbulence and the dust disk in IM Lup: Onset of planetesimal formation. , keywords =. doi:10.1051/0004-6361/202244869 , archivePrefix =. 2212.01291 , primaryClass =

    work page doi:10.1051/0004-6361/202244869

  43. [43]

    , keywords =

    Turbulence in protoplanetary disks: A systematic analysis of dust settling in 33 disks. , keywords =. doi:10.1051/0004-6361/202553822 , archivePrefix =. 2503.05872 , primaryClass =

    work page doi:10.1051/0004-6361/202553822

  44. [44]

    , keywords =

    Protoplanetary Disk Chemistry. , keywords =. doi:10.1146/annurev-astro-022823-040820 , archivePrefix =. 2309.05685 , primaryClass =

    work page doi:10.1146/annurev-astro-022823-040820

  45. [45]

    , keywords =

    Impact of size-dependent grain temperature on gas-grain chemistry in protoplanetary disks: The case of low-mass star disks. , keywords =. doi:10.1051/0004-6361/202038788 , archivePrefix =. 2106.05888 , primaryClass =

    work page doi:10.1051/0004-6361/202038788

  46. [46]

    OpTool: Command-line driven tool for creating complex dust opacities

  47. [47]

    ALMA reveals the anatomy of the mm-sized dust and molecular gas in the HD 97048 disk

    ALMA Reveals the Anatomy of the mm-sized Dust and Molecular Gas in the HD 97048 Disk. , keywords =. doi:10.3847/0004-637X/831/2/200 , archivePrefix =. 1609.02011 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/0004-637x/831/2/200

  48. [48]

    Passive irradiated circumstellar disks with an inner hole

    Passive Irradiated Circumstellar Disks with an Inner Hole. , keywords =. doi:10.1086/323057 , archivePrefix =. astro-ph/0106470 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/323057

  49. [49]

    exoALMA. IV. Substructures, Asymmetries, and the Faint Outer Disk in Continuum Emission. , keywords =. doi:10.3847/2041-8213/adc438 , archivePrefix =. 2504.18725 , primaryClass =

    work page doi:10.3847/2041-8213/adc438 2041

  50. [50]

    Dust modeling of the combined ALMA and SPHERE datasets of HD163296. Is HD163296 really a Meeus group II disk?

    Dust modeling of the combined ALMA and SPHERE datasets of HD 163296. Is HD 163296 really a Meeus group II disk?. , keywords =. doi:10.1051/0004-6361/201732299 , archivePrefix =. 1802.03328 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201732299

  51. [51]

    Radiative transfer in very optically thick circumstellar disks

    Radiative transfer in very optically thick circumstellar disks. , keywords =. doi:10.1051/0004-6361/200811470 , archivePrefix =. 0902.3092 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/200811470

  52. [52]

    , keywords =

    Investigating the Relative Gas and Small Dust Grain Surface Heights in Protoplanetary Disks. , keywords =. doi:10.3847/1538-4357/abf92e , archivePrefix =. 2104.07821 , primaryClass =

    work page doi:10.3847/1538-4357/abf92e

  53. [53]

    Effect of dust size and structure on scattered light images of protoplanetary discs

    Effect of dust size and structure on scattered-light images of protoplanetary discs. , keywords =. doi:10.1093/mnras/stz662 , archivePrefix =. 1903.01890 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1093/mnras/stz662 1903

  54. [54]

    , keywords =

    Fractal Aggregates of Submicron-sized Grains in the Young Planet-forming Disk around IM Lup. , keywords =. doi:10.3847/2041-8213/acb824 , archivePrefix =. 2302.01119 , primaryClass =

    work page doi:10.3847/2041-8213/acb824 2041

  55. [55]

    Scattered light mapping of protoplanetary disks

    Scattered light mapping of protoplanetary disks. , keywords =. doi:10.1051/0004-6361/201629098 , archivePrefix =. 1609.09505 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201629098

  56. [56]

    Disk Evolution Study Through Imaging of Nearby Young Stars (DESTINYS): V721 CrA and BN CrA have wide and structured disks in polarised IR

    Disk Evolution Study Through Imaging of Nearby Young Stars (DESTINYS): V721 CrA and BN CrA have wide and structured disks in the polarised infrared. , keywords =. doi:10.1051/0004-6361/202556331 , archivePrefix =. 2511.01717 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/202556331

  57. [57]

    , keywords =

    DRAGyS A comprehensive tool for extracting scattering phase functions in protoplanetary disks: Disk ring adjusted geometry yields scattering phase function. , keywords =. doi:10.1051/0004-6361/202554058 , archivePrefix =. 2505.20070 , primaryClass =

    work page doi:10.1051/0004-6361/202554058

  58. [58]

    Protostars and Planets VII , year = 2023, editor =

    Optical and Near-infrared View of Planet-forming Disks and Protoplanets. Protostars and Planets VII , year = 2023, editor =. doi:10.48550/arXiv.2203.09991 , archivePrefix =. 2203.09991 , primaryClass =

    work page doi:10.48550/arxiv.2203.09991 2023

  59. [59]

    Shadows and cavities in protoplanetary disks: HD163296, HD141569A, and HD150193A in polarized light

    Shadows and cavities in protoplanetary disks: HD 163296, HD 141569A, and HD 150193A in polarized light. , keywords =. doi:10.1051/0004-6361/201424262 , archivePrefix =. 1406.7387 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201424262

  60. [60]

    Direct Imaging of Fine Structures in Giant Planet Forming Regions of the Protoplanetary Disk around AB Aurigae

    Direct Imaging of Fine Structures in Giant Planet-forming Regions of the Protoplanetary Disk Around AB Aurigae. , keywords =. doi:10.1088/2041-8205/729/2/L17 , archivePrefix =. 1102.4408 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/2041-8205/729/2/l17 2041

  61. [61]

    Proceedings of the Japan Academy, Series B , year = 2016, month = feb, volume =

    SEEDS - Strategic explorations of exoplanets and disks with the Subaru Telescope -. Proceedings of the Japan Academy, Series B , year = 2016, month = feb, volume =. doi:10.2183/pjab.92.45 , adsurl =

    work page doi:10.2183/pjab.92.45 2016

  62. [62]

    , keywords =

    Gemini-LIGHTS: Herbig Ae/Be and Massive T Tauri Protoplanetary Disks Imaged with Gemini Planet Imager. , keywords =. doi:10.3847/1538-3881/ac7be4 , archivePrefix =. 2206.05815 , primaryClass =

    work page doi:10.3847/1538-3881/ac7be4

  63. [63]

    , keywords =

    Disk Evolution Study Through Imaging of Nearby Young Stars (DESTINYS): Late Infall Causing Disk Misalignment and Dynamic Structures in SU Aur. , keywords =. doi:10.3847/2041-8213/abdf57 , archivePrefix =. 2102.08781 , primaryClass =

    work page doi:10.3847/2041-8213/abdf57 2041

  64. [64]

    Multiple rings in the transition disk and companion candidates around RXJ1615.3-3255. High contrast imaging with VLT/SPHERE

    Multiple rings in the transition disk and companion candidates around RX J1615.3-3255. High contrast imaging with VLT/SPHERE. , keywords =. doi:10.1051/0004-6361/201629267 , archivePrefix =. 1610.04038 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201629267

  65. [65]

    Spectral Energy Distributions of T Tauri Stars With Passive Circumstellar Disks

    Spectral Energy Distributions of T Tauri Stars with Passive Circumstellar Disks. , keywords =. doi:10.1086/304869 , archivePrefix =. astro-ph/9706042 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/304869

  66. [66]

    Protostars and Planets VII , year = 2023, editor =

    Planet Formation Theory in the Era of ALMA and Kepler: from Pebbles to Exoplanets. Protostars and Planets VII , year = 2023, editor =. doi:10.48550/arXiv.2203.09759 , archivePrefix =. 2203.09759 , primaryClass =

    work page doi:10.48550/arxiv.2203.09759 2023

  67. [67]

    The Flying Saucer: Tomography of the thermal and density gas structure of an edge-on protoplanetary disk

    The Flying Saucer: Tomography of the thermal and density gas structure of an edge-on protoplanetary disk. , keywords =. doi:10.1051/0004-6361/201730645 , archivePrefix =. 1706.02608 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201730645

  68. [68]

    The Anatomy of an Unusual Edge-on Protoplanetary Disk. II. Gas Temperature and a Warm Outer Region. , keywords =. doi:10.3847/1538-3881/abeb1e , archivePrefix =. 2103.02666 , primaryClass =

    work page doi:10.3847/1538-3881/abeb1e

  69. [69]

    , keywords =

    Imaging the LkCa 15 system in polarimetry and total intensity without self-subtraction artefacts. , keywords =. doi:10.1051/0004-6361/202449743 , archivePrefix =. 2512.18439 , primaryClass =

    work page doi:10.1051/0004-6361/202449743

  70. [70]

    The circumstellar disk HD$\,$169142: gas, dust and planets acting in concert?

    The Circumstellar Disk HD 169142: Gas, Dust, and Planets Acting in Concert?. , keywords =. doi:10.3847/1538-4357/aa94c2 , archivePrefix =. 1710.06485 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/aa94c2

  71. [71]

    The Disk Substructures at High Angular Resolution Project (DSHARP). I. Motivation, Sample, Calibration, and Overview. , keywords =. doi:10.3847/2041-8213/aaf741 , archivePrefix =. 1812.04040 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/2041-8213/aaf741 2041

  72. [72]

    Physical and Chemical Structure of Protoplanetary Disks with Grain Growth

    Physical and Chemical Structure of Protoplanetary Disks with Grain Growth. , keywords =. doi:10.1086/501114 , archivePrefix =. astro-ph/0601230 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1086/501114

  73. [73]

    Consistent dust and gas models for protoplanetary disks. I. Disk shape, dust settling, opacities, and PAHs. , keywords =. doi:10.1051/0004-6361/201526538 , archivePrefix =. 1511.03431 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201526538

  74. [74]

    Impact of grain evolution on the chemical structure of protoplanetary disks

    Impact of Grain Evolution on the Chemical Structure of Protoplanetary Disks. , keywords =. doi:10.1088/0004-637X/727/2/76 , archivePrefix =. 1011.4420 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0004-637x/727/2/76

  75. [75]

    The warm gas atmosphere of the HD 100546 disk seen by Herschel (Evidence of a gas-rich, carbon-poor atmosphere?)

    The warm gas atmosphere of the HD 100546 disk seen by Herschel. Evidence of a gas-rich, carbon-poor atmosphere?. , keywords =. doi:10.1051/0004-6361/201118218 , archivePrefix =. 1201.4860 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201118218

  76. [76]

    Survival of molecular gas in cavities of transition disks. I. CO. , keywords =. doi:10.1051/0004-6361/201321171 , archivePrefix =. 1308.2966 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201321171

  77. [77]

    Determining protoplanetary disk gas masses from CO isotopologues line observations

    Determining protoplanetary disk gas masses from CO isotopologues line observations. , keywords =. doi:10.1051/0004-6361/201628159 , archivePrefix =. 1605.07780 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1051/0004-6361/201628159

  78. [78]

    , keywords =

    Beyond diffusion: a generalized mean-field theory of turbulent dust transport in protoplanetary discs. , keywords =. doi:10.1093/mnras/stad2471 , archivePrefix =. 2306.06103 , primaryClass =

    work page doi:10.1093/mnras/stad2471

  79. [79]

    Particle Stirring in Turbulent Gas Disks: Including Orbital Oscillations

    Particle stirring in turbulent gas disks: Including orbital oscillations. , keywords =. doi:10.1016/j.icarus.2007.07.012 , archivePrefix =. 0707.2975 , primaryClass =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.icarus.2007.07.012 2007

  80. [80]

    exoALMA. XV. Interpreting the Height of CO Emission Layer. , keywords =. doi:10.3847/2041-8213/adc42e , archivePrefix =. 2504.20012 , primaryClass =

    work page doi:10.3847/2041-8213/adc42e 2041

Showing first 80 references.