pith. sign in

arxiv: 2605.23680 · v1 · pith:LRTN6Y6Enew · submitted 2026-05-22 · 🌌 astro-ph.EP

Modeling (Sub-)millimeter Scattering Properties of Fractal and Consolidated Porous Particles: Applications to Protoplanetary Disks

Gonzalo Vargas (1) , Daniel Guirado (1) , Carlos Carrasco-Gonzalez (2) , Olga Munoz (1) , Maxim A. Yurkin (3) , Enrique Macias (4) , Jesus M. Jaquez-Dominguez (2) , Francisco J. Garcia-Izquierdo (1) ((1) Instituto de Astrofisica de Andalucia (IAA-CSIC)
show 15 more authors
Granada Spain (2) Instituto de Radioastronomia y Astrofisica Universidad Nacional Autonoma de Mexico Morelia Mexico (3) Universite Rouen Normandie INSA Rouen Normandie CNRS CORIA UMR 6614 Saint-Etienne-du-Rouvray France (4) European Southern Observatory (ESO) Garching bei Muenchen Germany)
This is my paper

Pith reviewed 2026-05-25 02:38 UTC · model grok-4.3

classification 🌌 astro-ph.EP
keywords protoplanetary disksdust scatteringporous particlesmillimeter wavelengthspolarizationabsorption opacityfractal aggregatesplanet formation
0
0 comments X

The pith

Porous dust particles in protoplanetary disks strengthen forward scattering and polarization while lowering absorption per unit mass compared to compact spheres.

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

The paper computes scattering properties for two populations of porous dust using numerical methods and DSHARP optical constants at wavelengths from 0.87 to 10 mm. It establishes that higher porosity increases forward scattering and polarization near 90 degrees, allowing maximum particle sizes around 1 mm to remain consistent with observed polarization levels. Porosity simultaneously reduces the absorption cross section at fixed dust mass, which means observed continuum fluxes correspond to larger total dust masses than compact-sphere calculations would suggest. A sympathetic reader would care because these optical changes directly alter how astronomers convert millimeter observations into estimates of particle sizes and solid masses available for planet formation.

Core claim

Using the discrete dipole approximation for consolidated porous particles and the multiple-sphere T-matrix method for fractal and hierarchical aggregates, the calculations show that increasing porosity strengthens forward scattering and enhances polarization near 90 degrees relative to compact spheres. For a size distribution with power-law index -3.5, porous particles maintain a broader peak in the product of polarization at 90 degrees and effective albedo that extends to larger sizes, keeping polarization-based constraints compatible with maximum sizes near 1 mm. Porosity also lowers the absorption opacity at fixed dust mass relative to compact spheres, implying larger inferred dust masses

What carries the argument

Porosity in consolidated porous particles and fractal/hierarchical aggregates, which modifies the computed scattering matrices, cross sections, and effective albedo for a power-law size distribution at sub-millimeter to millimeter wavelengths.

If this is right

  • Polarization observations remain compatible with maximum grain sizes of order 1 mm when porosity is taken into account.
  • Absorption opacity decreases with increasing porosity, requiring upward revisions to dust mass estimates derived from millimeter continuum fluxes.
  • Stronger forward scattering redistributes light differently across the disk at these wavelengths.
  • The broader size range over which significant polarization persists affects how multi-wavelength data are interpreted for grain growth.

Where Pith is reading between the lines

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

  • If real disk dust exhibits comparable porosity, current mass estimates for protoplanetary disks may be systematically underestimated, increasing the solid reservoir available for planet formation.
  • The models predict testable differences in polarization spectra across wavelengths that could be checked with high-resolution observations.
  • Accounting for particle structure may help reconcile apparent tensions between size limits inferred from polarization and those from spectral indices.

Load-bearing premise

The chosen particle models of consolidated porous particles and fractal aggregates together with the DSHARP optical constants accurately represent the actual dust populations in protoplanetary disks.

What would settle it

Observations that show polarization at 90 degrees times effective albedo declining sharply once particle sizes exceed half the wavelength over pi, or that absorption opacities match compact-sphere values even for porous structures.

Figures

Figures reproduced from arXiv: 2605.23680 by (2) Instituto de Radioastronomia y Astrofisica, (3) Universite Rouen Normandie, (4) European Southern Observatory (ESO), Carlos Carrasco-Gonzalez (2), CNRS, CORIA UMR 6614, Daniel Guirado (1), Enrique Macias (4), France, Francisco J. Garcia-Izquierdo (1) ((1) Instituto de Astrofisica de Andalucia (IAA-CSIC), Garching bei Muenchen, Germany), Gonzalo Vargas (1), Granada, INSA Rouen Normandie, Jesus M. Jaquez-Dominguez (2), Maxim A. Yurkin (3), Mexico, Morelia, Olga Munoz (1), Saint-Etienne-du-Rouvray, Spain, Universidad Nacional Autonoma de Mexico.

Figure 1
Figure 1. Figure 1: Representative consolidated porous (CP) particle models computed with ADDA. Porosity increases from left to right, from P = 0.3 to 0.9. All particles are scaled to the same radius of an equivalent-volume sphere, a = 100 µm. The corresponding mass opacities are κsca = Csca mdust , κabs = Cabs mdust , κext = Cext mdust , (6) where mdust is the mass of the particle. The single-scattering albedo is ω¯ = Csca C… view at source ↗
Figure 2
Figure 2. Figure 2: Representative aggregate models computed with MSTM. From left to right: Case I, a fractal aggregate (FA) with Df = 2.7 and kf = 0.3; Case II, an FA with Df = 2.1 and kf = 0.7; and Case III, a hierarchical aggregate (HA) built from 64 randomly oriented sub-aggregates, each containing 128 monomers with Df = 1.2 and kf = 1.0. All three cases have the same radius of an equivalent-volume sphere, a = 100 µm. 2.4… view at source ↗
Figure 3
Figure 3. Figure 3: Size-averaged scattering properties for the adopted size distribution. The upper rows show the phase function F11(θ) and the lower rows show the linear polarization fraction −F12(θ)/F11(θ) from λ = 0.87 to 10 mm for compact spheres (CS), consolidated porous particles (CP; P = 0.50, 0.70, and 0.90), and MSTM aggregate models (FA with P = 0.94 and HA with P = 0.99). For the MSTM aggregate models, results up … view at source ↗
Figure 4
Figure 4. Figure 4: Size-averaged mass opacities for a size distribution with amin = 0.1 µm, shown as functions of the maximum particle size amax at four representative wavelengths, λ = 0.87, 1.0, 3.0, and 7.0 mm. Top panels: scattering opacity κsca (dotted) together with the effective scattering opacity κsca,eff (solid). Middle panels: absorption opacity κabs. Bottom panels: extinction opacity κext (dotted) together with κex… view at source ↗
Figure 5
Figure 5. Figure 5: Spectral behavior of the size-averaged mass opacities for a size distribution with amin = 0.1 µm. Left and right columns correspond to amax = 100 µm and amax = 1 mm, respectively. Top panels: scattering opacity κsca (dotted) together with the effective scattering opacity κsca,eff (solid). Middle panels: absorption opacity κabs. Bottom panels: extinction opacity κext (dotted) together with κext,eff (solid).… view at source ↗
Figure 6
Figure 6. Figure 6: P(90◦ ) ¯ω (dotted) and P(90◦ ) ¯ωeff (solid) as functions of the maximum particle size amax for a power-law size distribution, n(a) ∝ a −3.5 , with amin = 0.1 µm. The panels span λ = 0.87–10 mm. For the MSTM aggregate models, calculations up to amax = 1 mm are available only at λ = 0.87, 1.0, 3.0, and 7.0 mm. 4.3. Polarized Scattered Emission [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Spectral behavior of P(90◦ ) ¯ω (dotted) and P(90◦ ) ¯ωeff (solid) for a size distribution with amin = 0.1 µm and amax = 100 µm (left) or 1 mm (right). The same particle morphologies as in [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: P(90◦ ) ¯ωeff for λ = 0.87 mm (top), 1.0 mm (middle), and 3.0 mm (bottom). Solid lines show the results for compact spheres and porous particles: CP with P = 0.70 and 0.90, and HA with P = 0.99. Dotted lines show the Mie–EMA models for P = 0.70, 0.90, and 0.99, obtained by applying the Bruggeman rule to the DSHARP composition. ω¯eff closely follows ¯ω, with the largest reductions for P = 0.94–0.99. For ama… view at source ↗
read the original abstract

We perform light-scattering numerical simulations for two dust populations: (i) consolidated porous particles computed with the discrete dipole approximation (ADDA) and (ii) highly porous aggregate models, including fractal and hierarchical aggregates, computed with the multiple-sphere T-matrix method (MSTM). Using DSHARP optical constants, we compute scattering matrices, cross sections, and effective albedo omega_eff for a size distribution n(a) proportional to a^q, with q = -3.5, amin = 0.1 micron, and ten wavelengths from 0.87 to 10 mm. We find that increasing porosity strengthens forward scattering and enhances polarization near theta approximately 90 degrees. For compact spheres, P(90 degrees) times omega_eff peaks near amax approximately lambda divided by 2 pi and then declines, whereas porous particles show a broader peak extending to larger sizes, keeping polarization-based constraints compatible with amax approximately 1 mm. Porosity also lowers kappa_abs at fixed dust mass relative to compact spheres, implying larger inferred dust masses for a given continuum flux.

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 performs light-scattering simulations for consolidated porous particles (via ADDA/DDA) and fractal/hierarchical aggregates (via MSTM) using DSHARP refractive indices. For a power-law size distribution n(a) ∝ a^{-3.5} with a_min = 0.1 μm at ten wavelengths from 0.87–10 mm, it reports that increasing porosity strengthens forward scattering, raises P(90°) near 90°, broadens the peak of P(90°)ω_eff to larger a_max (keeping ~1 mm sizes compatible with polarization data), and lowers κ_abs at fixed dust mass relative to compact spheres, implying larger inferred dust masses from a given continuum flux.

Significance. If the numerical results are robust, the work is significant for protoplanetary-disk studies because it supplies a concrete physical mechanism that can reconcile millimeter polarization constraints with a_max ~ 1 mm while directly affecting mass estimates from continuum fluxes. The use of two independent, established scattering codes on the same optical constants is a methodological strength that allows internal cross-checks.

major comments (2)
  1. [§2 and §3] §2 (Numerical methods) and §3 (Results): the manuscript reports quantitative changes in κ_abs, ω_eff, and scattering-matrix elements but supplies no convergence tests, dipole-resolution studies, multipole-truncation criteria, or validation against Mie theory for the compact-sphere limit; these omissions are load-bearing for the claimed differences between porous and compact cases.
  2. [§4] §4 (Discussion): the implication that inferred dust masses increase because κ_abs is lower at fixed mass follows algebraically from the definition κ_abs = C_abs/m once the DDA/MSTM runs are accepted, but the paper does not quantify the magnitude of the change or its sensitivity to the precise porosity parameterization, weakening the observational claim.
minor comments (2)
  1. [Figures] Figure captions should explicitly state the number of realizations or orientations averaged for the aggregate models.
  2. [§2] The definition of effective albedo ω_eff appears only in the abstract; it should be introduced with an equation in the methods section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and will revise the manuscript to incorporate the requested additions.

read point-by-point responses

  1. Referee: [§2 and §3] §2 (Numerical methods) and §3 (Results): the manuscript reports quantitative changes in κ_abs, ω_eff, and scattering-matrix elements but supplies no convergence tests, dipole-resolution studies, multipole-truncation criteria, or validation against Mie theory for the compact-sphere limit; these omissions are load-bearing for the claimed differences between porous and compact cases.

    Authors: We agree that explicit convergence tests and validation against Mie theory are necessary to substantiate the numerical results. In the revised manuscript we will add a new subsection in §2 that reports dipole-resolution studies for ADDA, multipole-truncation criteria for MSTM, and direct comparisons of the compact-sphere limit to Mie calculations using identical optical constants. These tests will be performed at the wavelengths and size parameters used in the study. revision: yes

  2. Referee: [§4] §4 (Discussion): the implication that inferred dust masses increase because κ_abs is lower at fixed mass follows algebraically from the definition κ_abs = C_abs/m once the DDA/MSTM runs are accepted, but the paper does not quantify the magnitude of the change or its sensitivity to the precise porosity parameterization, weakening the observational claim.

    Authors: We acknowledge that quantifying the factor by which inferred dust masses increase and testing sensitivity to the porosity parameterization would strengthen the observational implications. The revised discussion will include explicit numerical factors for the reduction in κ_abs at selected wavelengths and porosities, together with a brief exploration of how the mass correction varies with the adopted porosity model. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper reports direct numerical computations of scattering matrices, cross sections, and opacities via ADDA and MSTM codes applied to specified particle geometries, DSHARP refractive indices, and a fixed power-law size distribution n(a) ~ a^{-3.5}. The lowering of kappa_abs at fixed dust mass is an algebraic consequence of the definition kappa_abs = C_abs / m once the cross sections are obtained for the porous structures; no parameter is fitted to data and then relabeled as a prediction, no self-citation supplies a uniqueness theorem or ansatz, and no equation is defined in terms of its own output. All reported trends (forward scattering, polarization peak width, mass inference) are therefore independent numerical results rather than tautological reductions.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claims rest on the numerical accuracy of ADDA and MSTM for the chosen particle models, the applicability of DSHARP optical constants to disk dust, and the representativeness of the power-law size distribution with fixed q and amin.

free parameters (2)
  • q = -3.5
    Power-law index of the size distribution n(a) proportional to a^q set to -3.5.
  • amin = 0.1 micron
    Minimum particle radius in the size distribution set to 0.1 micron.
axioms (1)
  • domain assumption DSHARP optical constants accurately represent the refractive indices of dust in protoplanetary disks.
    Used as fixed input for all scattering calculations across wavelengths.

pith-pipeline@v0.9.0 · 5880 in / 1379 out tokens · 25766 ms · 2026-05-25T02:38:41.818803+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

73 extracted references · 65 canonical work pages · 3 internal anchors

  1. [1]

    and Lazarian, A

    Andersson, B.-G. and Lazarian, A. and Vaillancourt, John E. , title =. , year =. doi:10.1146/annurev-astro-082214-122414 , adsurl =

    work page doi:10.1146/annurev-astro-082214-122414

  2. [2]

    Andrews, S. M. and Huang, J. and P\'erez, L. M. and Isella, A. and Dullemond, C. P. and Kurtovic, N. T. and Guzm\'an, V. V. and Carpenter, J. M. and Wilner, D. J. and Zhang, S. and Zhu, Z. and Birnstiel, T. and Bai, X.-N. and Benisty, M. and Hughes, A. M. and \"Oberg, K. I. and Ricci, L. , title =. , year =. doi:10.3847/2041-8213/aaf741 , adsurl =

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

  3. [3]

    Andrews, S. M. , title =. , year =. doi:10.1146/annurev-astro-031220-010302 , adsurl =

    work page doi:10.1146/annurev-astro-031220-010302

  4. [4]

    and Quanz, S

    Avenhaus, H. and Quanz, S. P. and Garufi, A. and P\'erez, S. and Casassus, S. and Pinte, C. and Bertrang, G. H.-M. and C\'aceres, C. and Benisty, M. and Dominik, C. , title =. , year =. doi:10.3847/1538-4357/aab846 , adsurl =

    work page doi:10.3847/1538-4357/aab846

  5. [5]

    , year =

    Birnstiel, Tilman , title =. , year =. doi:10.1146/annurev-astro-071221-052705 , adsurl =

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

  6. [6]

    and Dullemond, C

    Birnstiel, T. and Dullemond, C. P. and Zhu, Z. and Andrews, S. M. and Bai, X.-N. and Wilner, D. J. and Carpenter, J. M. and Huang, J. and Isella, A. and Benisty, M. and P. The Disk Substructures at High Angular Resolution Project (. , year =. doi:10.3847/2041-8213/aaf743 , adsurl =

    work page doi:10.3847/2041-8213/aaf743 2041

  7. [7]

    and Huffman, Donald R

    Bohren, Craig F. and Huffman, Donald R. , title =. 1983 , doi =

    1983

  8. [8]

    and Dullemond, C

    Brauer, F. and Dullemond, C. P. and Henning, Th. , title =. , year =. doi:10.1051/0004-6361:20077759 , adsurl =

    work page doi:10.1051/0004-6361:20077759

  9. [9]

    The Radial Distribution of Dust Particles in the HL Tau Disk from

    Carrasco-Gonz. The Radial Distribution of Dust Particles in the HL Tau Disk from. , year =. doi:10.3847/1538-4357/ab3d33 , adsurl =

    work page doi:10.3847/1538-4357/ab3d33

  10. [10]

    , year =

    D'Alessio, Paola and Calvet, Nuria and Hartmann, Lee , title =. , year =. doi:10.1086/320655 , adsurl =

    work page doi:10.1086/320655

  11. [11]

    Draine, B. T. , title =. , year =. doi:10.1146/annurev.astro.41.011802.094840 , adsurl =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1146/annurev.astro.41.011802.094840

  12. [12]

    P., et al., 2018, @doi [ ] 10.3847/2041-8213/aaf742 , http://adsabs.harvard.edu/abs/2018ApJ...869L..46D 869, L46

    Dullemond, Cornelis P. and Birnstiel, Tilman and Huang, Jane and Kurtovic, Nicol. The Disk Substructures at High Angular Resolution Project (. , year =. doi:10.3847/2041-8213/aaf742 , adsurl =

    work page doi:10.3847/2041-8213/aaf742 2041

  13. [13]

    Estrada, P. R. and Cuzzi, J. N. and Umurhan, O. M. , title =. , year =. doi:10.3847/1538-4357/ac7ffd , adsurl =

    work page doi:10.3847/1538-4357/ac7ffd

  14. [14]

    Farias, T. L. and K. Range of validity of the. , year =. doi:10.1364/AO.35.006560 , adsurl =

    work page doi:10.1364/ao.35.006560

  15. [15]

    Filippov, A. V. and Zurita, M. and Rosner, D. E. , title =. J. Colloid Interface Sci. , year =. doi:10.1006/jcis.2000.7027 , adsurl =

    work page doi:10.1006/jcis.2000.7027 2000

  16. [16]

    and Pascucci, Ilaria and Rosotti, Giovanni and Zagaria, Francesco and Clarke, Cathie and Herczeg, Gregory J

    Garufi, Antonio and Carrasco-Gonzalez, Carlos and Macias, Enrique and Testi, Leonardo and Curone, Pietro and Ricci, Luca and Facchini, Stefano and Long, Feng and Manara, Carlo F. and Pascucci, Ilaria and Rosotti, Giovanni and Zagaria, Francesco and Clarke, Cathie and Herczeg, Gregory J. and Isella, Andrea and Rota, Alessia and Mauco, Karina and van der Ma...

    work page doi:10.1051/0004-6361/202452496

  17. [17]

    and Tazaki, R

    Ginski, C. and Tazaki, R. and Dominik, C. and Stolker, T. , title =. , year =. doi:10.3847/1538-4357/acdc97 , adsurl =

    work page doi:10.3847/1538-4357/acdc97

  18. [18]

    and Travis, Larry D

    Hansen, James E. and Travis, Larry D. , title =. SSRv , year =

  19. [19]

    2012 , edition =

    Hapke, Bruce , title =. 2012 , edition =

    2012

  20. [20]

    Harris, K

    Harris, Charles R. and Millman, K. Jarrod and van der Walt, St. Array programming with. Nature , year =. doi:10.1038/s41586-020-2649-2 , adsurl =

    work page doi:10.1038/s41586-020-2649-2

  21. [21]

    and Stognienko, R

    Henning, Th. and Stognienko, R. , title =. , year =

  22. [22]

    , title =

    Henning, T. , title =. , year =. doi:10.1146/annurev-astro-081309-130815 , adsurl =

    work page doi:10.1146/annurev-astro-081309-130815

  23. [23]

    Hunter, J. D. , title =. Comput. Sci. Eng. , year =

  24. [24]

    Exploring Polarized Millimeter Emission from Protoplanetary Disks with Irregular Dust Grains

    Exploring Polarized Millimeter Emission from Protoplanetary Disks with Irregular Dust Grains. , year = 2026, month = apr, eid =. doi:10.48550/arXiv.2604.17779 , adsurl =

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2604.17779 2026

  25. [25]

    and Muto, T

    Kataoka, A. and Muto, T. and Momose, M. and Tsukagoshi, T. and Fukagawa, M. and Shibai, H. and Hanawa, T. and Murakawa, K. and Dullemond, C. P. , title =. , year =. doi:10.1088/0004-637X/809/1/78 , adsurl =

    work page doi:10.1088/0004-637x/809/1/78

  26. [26]

    W., Tomisaka K., Momose M., 2017, @doi [ ] 10.3847/2041-8213/aa7e33 , http://adsabs.harvard.edu/abs/2017ApJ...844L...5K 844, L5

    Kataoka, Akimasa and Tsukagoshi, Takashi and Pohl, Adriana and Muto, Takayuki and Nagai, Hiroshi and Stephens, Ian W. and Tomisaka, Kohji and Momose, Munetake , title =. , year =. doi:10.3847/2041-8213/aa7e33 , adsurl =

    work page doi:10.3847/2041-8213/aa7e33 2041

  27. [27]

    and Flock, Mario , title =

    Kirchschlager, Florian and Bertrang, Gesa H.-M. and Flock, Mario , title =. , year =. doi:10.1093/mnras/stz1763 , adsurl =

    work page doi:10.1093/mnras/stz1763

  28. [28]

    , title =

    Kirchschlager, Florian and Bertrang, Gesa H.-M. , title =. , year =. doi:10.1051/0004-6361/202037943 , adsurl =

    work page doi:10.1051/0004-6361/202037943

  29. [29]

    , year =

    Kirchschlager, Florian and Wolf, Sebastian , title =. , year =. doi:10.1051/0004-6361/201323176 , adsurl =

    work page doi:10.1051/0004-6361/201323176

  30. [30]

    2018 , volume =

    Light scattering by hierarchical aggregates , journal =. 2018 , volume =

    2018

  31. [31]

    and Stephens, Ian W

    Lin, Zhe-Yu Daniel and Li, Zhi-Yun and Yang, Haifeng and Mu\ noz, Olga and Looney, Leslie W. and Stephens, Ian W. and Hull, Charles L. H. and Fern\'andez-L\'opez, Manuel and Harrison, Rachel , title =. , year =. doi:10.1093/mnras/stad173 , adsurl =

    work page doi:10.1093/mnras/stad173

  32. [32]

    Lin, Z.-Y. D. and Li, Z.-Y. and Stephens, I. W. and Fern. Panchromatic (Sub)millimeter Polarization Observations of HL Tau Unveil Aligned Scattering Grains , journal =. 2024 , volume =. doi:10.1093/mnras/stae040 , adsurl =

    work page doi:10.1093/mnras/stae040 2024

  33. [33]

    and Linz, H

    Liu, Y. and Linz, H. and Fang, M. and Henning, T. and Wolf, S. and Flock, M. and Rosotti, G. P. and Wang, H. and Li, D. , title =. , year =. doi:10.1051/0004-6361/202244505 , adsurl =

    work page doi:10.1051/0004-6361/202244505

  34. [34]

    , year =

    Liu, Yao and Roussel, H\'el\`ene and Linz, Hendrik and Fang, Min and Wolf, Sebastian and Kirchschlager, Florian and Henning, Thomas and Yang, Haifeng and Du, Fujun and Flock, Mario and Wang, Hongchi , title =. , year =. doi:10.1051/0004-6361/202451981 , adsurl =

    work page doi:10.1051/0004-6361/202451981

  35. [35]

    Characterizing the dust content of disk substructures in TW Hydrae , journal =

    Mac. Characterizing the dust content of disk substructures in TW Hydrae , journal =. 2021 , volume =. doi:10.1051/0004-6361/202039812 , adsurl =

    work page doi:10.1051/0004-6361/202039812 2021

  36. [36]

    and Mishchenko, Michael I

    Mackowski, Daniel W. and Mishchenko, Michael I. , title =. JQSRT , year =. doi:10.1016/j.jqsrt.2011.02.019 , adsurl =

    work page doi:10.1016/j.jqsrt.2011.02.019 2011

  37. [37]

    Mathis, J. S. and Rumpl, W. and Nordsieck, K. H. , title =. , year =. doi:10.1086/155591 , adsurl =

    work page doi:10.1086/155591

  38. [38]

    Multiwavelength optical properties of compact dust aggregates in protoplanetary disks , journal =

    Min, Michiel and Rab, Christian and Woitke, Peter and Dominik, Cornelis and M. Multiwavelength optical properties of compact dust aggregates in protoplanetary disks , journal =. 2016 , volume =. doi:10.1051/0004-6361/201526048 , adsurl =

    work page doi:10.1051/0004-6361/201526048 2016

  39. [39]

    2000 , address =

    Light Scattering by Nonspherical Particles: Theory, Measurements, and Applications , publisher =. 2000 , address =

    2000

  40. [40]

    and Yurkin, Maxim A

    Mishchenko, Michael I. and Yurkin, Maxim A. , title =. Opt. Lett. , year =. doi:10.1364/OL.42.000494 , adsurl =

    work page doi:10.1364/ol.42.000494

  41. [41]

    and Guirado, D

    Moreno, F. and Guirado, D. and Mu. Models of Rosetta/OSIRIS 67P Dust Coma Phase Function , journal =. 2018 , volume =. doi:10.3847/1538-3881/aae526 , adsurl =

    work page doi:10.3847/1538-3881/aae526 2018

  42. [42]

    2019 , version =

    Moteki, Nobuhiro , title =. 2019 , version =. doi:10.5281/zenodo.3567236 , url =

    work page doi:10.5281/zenodo.3567236 2019

  43. [43]

    Experimental determination of scattering matrices of dust particles at visible wavelengths: The IAA light scattering apparatus , journal =

    Mu. Experimental determination of scattering matrices of dust particles at visible wavelengths: The IAA light scattering apparatus , journal =. 2010 , volume =. doi:10.1016/j.jqsrt.2009.06.011 , adsurl =

    work page doi:10.1016/j.jqsrt.2009.06.011 2010

  44. [44]

    Experimental Phase Function and Degree of Linear Polarization Curves of Millimeter-sized Cosmic Dust Analogs , journal =

    Mu. Experimental Phase Function and Degree of Linear Polarization Curves of Millimeter-sized Cosmic Dust Analogs , journal =. 2020 , volume =. doi:10.3847/1538-4365/ab6851 , adsurl =

    work page doi:10.3847/1538-4365/ab6851 2020

  45. [45]

    and Kenyon, Scott J

    Najita, Joan R. and Kenyon, Scott J. , title =. , year =. doi:10.1093/mnras/stu1994 , adsurl =

    work page doi:10.1093/mnras/stu1994

  46. [46]

    and Tanaka, H

    Okuzumi, S. and Tanaka, H. and Kobayashi, H. and Wada, K. , title =. , year =. doi:10.1088/0004-637X/752/2/106 , adsurl =

    work page doi:10.1088/0004-637x/752/2/106

  47. [47]

    2012 , publisher =

    Pitrou, Antoine , title =. 2012 , publisher =

    2012

  48. [48]

    P., Uribe A

    Pinilla, Paola and Birnstiel, Tilman and Ricci, Luca and Dullemond, Cornelis P. and Uribe, Ana and Testi, Leonardo and Natta, Antonella , title =. , year =. doi:10.1051/0004-6361/201118204 , adsurl =

    work page doi:10.1051/0004-6361/201118204

  49. [49]

    Potapov, Alexey and McCoustra, Martin R. S. and Tazaki, Ryo and Bergin, Edwin A. and Bromley, Stefan T. and Garrod, Robin T. and Rimola, Albert , title =. A&ARv , year =. doi:10.1007/s00159-025-00164-5 , adsurl =

    work page doi:10.1007/s00159-025-00164-5

  50. [50]

    and Testi, L

    Ricci, L. and Testi, L. and Natta, A. and Neri, R. and Cabrit, S. and Herczeg, G. J. , title =. , year =. doi:10.1051/0004-6361/200913403 , adsurl =

    work page doi:10.1051/0004-6361/200913403

  51. [51]

    and Lizano, S

    Sierra, A. and Lizano, S. , title =. , year =. doi:10.3847/1538-4357/ab7d32 , adsurl =

    work page doi:10.3847/1538-4357/ab7d32

  52. [52]

    and Wada, K

    Suyama, T. and Wada, K. and Tanaka, H. and Okuzumi, S. , title =. , year =. doi:10.1088/0004-637X/753/2/115 , adsurl =

    work page doi:10.1088/0004-637x/753/2/115

  53. [53]

    W., et al., 2014, @doi [ ] 10.1038/nature13850 , http://adsabs.harvard.edu/abs/2014Natur.514..597S 514, 597

    Stephens, Ian W. and Looney, Leslie W. and Kwon, Woojin and Fern. Spatially Resolved Magnetic Field Structure in the Disk of a T Tauri Star , journal =. 2014 , volume =. doi:10.1038/nature13850 , adsurl =

    work page doi:10.1038/nature13850 2014

  54. [54]

    and Lin, Zhe-Yu Daniel and Fern

    Stephens, Ian W. and Lin, Zhe-Yu Daniel and Fern. Aligned grains and scattered light found in gaps of planet-forming disk , journal =. 2023 , volume =. doi:10.1038/s41586-023-06648-7 , adsurl =

    work page doi:10.1038/s41586-023-06648-7 2023

  55. [55]

    , year =

    Tazaki, Ryo and Tanaka, Hidekazu and Okuzumi, Satoshi and Kataoka, Akimasa and Nomura, Hideko , title =. , year =. doi:10.3847/0004-637X/823/2/70 , adsurl =

    work page doi:10.3847/0004-637x/823/2/70

  56. [56]

    , year =

    Tazaki, Ryo and Lazarian, Alexandre and Nomura, Hideko , title =. , year =. doi:10.3847/1538-4357/839/1/56 , adsurl =

    work page doi:10.3847/1538-4357/839/1/56

  57. [57]

    and Tanaka, H

    Tazaki, R. and Tanaka, H. and Kataoka, A. and Okuzumi, S. and Muto, T. , title =. , year =. doi:10.3847/1538-4357/ab45f0 , adsurl =

    work page doi:10.3847/1538-4357/ab45f0

  58. [58]

    and Dominik, C

    Tazaki, R. and Dominik, C. , title =. , year =. doi:10.1051/0004-6361/202243485 , adsurl =

    work page doi:10.1051/0004-6361/202243485

  59. [59]

    , year =

    Tazaki, Ryo and Ginski, Christian and Dominik, Carsten , title =. , year =. doi:10.3847/2041-8213/acb824 , adsurl =

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

  60. [60]

    and Birnstiel, T

    Testi, L. and Birnstiel, T. and Ricci, L. and Andrews, S. and Blum, J. and Carpenter, J. and Dominik, C. and Isella, A. and Natta, A. and Williams, J. and Wilner, D. , editor =. Dust Evolution in Protoplanetary Disks , booktitle =. 2014 , pages =. doi:10.2458/azu_uapress_9780816531240-ch015 , address =

    work page doi:10.2458/azu_uapress_9780816531240-ch015 2014

  61. [61]

    and Kataoka, A

    Ueda, T. and Kataoka, A. and Zhang, S. and Zhu, Z. and Carrasco-Gonz\'alez, C. and Sierra, A. , title =. , year =. doi:10.3847/1538-4357/abf7b8 , adsurl =

    work page doi:10.3847/1538-4357/abf7b8

  62. [62]

    NatAs , year =

    Ueda, Takahiro and Tazaki, Ryo and Okuzumi, Satoshi and Flock, Mario and Sudarshan, Prakruti , title =. NatAs , year =. doi:10.1038/s41550-024-02308-6 , adsurl =

    work page doi:10.1038/s41550-024-02308-6

  63. [63]

    and Andrews, S

    Ueda, T. and Andrews, S. M. and Carrasco-Gonz\'alez, C. and Guerra-Alvarado, O. M. and Okuzumi, S. and Tazaki, R. and Kataoka, A. , title =. , year =. doi:10.3847/1538-4357/adf214 , adsurl =

    work page doi:10.3847/1538-4357/adf214

  64. [64]

    2026 , version =

    Gonzalo Vargas , title =. 2026 , version =. doi:10.5281/zenodo.19485482 , url =

    work page doi:10.5281/zenodo.19485482 2026

  65. [65]

    and Brandt, Richard E

    Warren, Stephen G. and Brandt, Richard E. , title =. JGR: Atmos. , year =. doi:10.1029/2007JD009744 , adsurl =

    work page doi:10.1029/2007jd009744

  66. [66]

    Weidenschilling, S. J. , title =. , year =. doi:10.1093/mnras/180.2.57 , adsurl =

    work page doi:10.1093/mnras/180.2.57

  67. [67]

    Wolff, M. J. and Clayton, G. C. and Martin, P. G. and Schulte-Ladbeck, R. E. , title =. , year =. doi:10.1086/173817 , adsurl =

    work page doi:10.1086/173817

  68. [68]

    Wolff, M. J. and Clayton, G. C. and Gibson, S. J. , title =. , year =. doi:10.1086/306029 , adsurl =

    work page doi:10.1086/306029

  69. [69]

    and Min, M

    Woitke, P. and Min, M. and Pinte, C. and Thi, W.-F. and Kamp, I. and Rab, C. and Anthonioz, F. and Antonellini, S. and Baldovin-Saavedra, C. and Carmona, A. and Dominik, C. and Dionatos, O. and Greaves, J. and G. Consistent dust and gas models for protoplanetary disks. I. Disk shape, dust settling, opacities, and PAHs , journal =. 2016 , volume =. doi:10....

    work page doi:10.1051/0004-6361/201526538 2016

  70. [70]

    and Stephens, Ian W

    Yang, Haifeng and Li, Zhi-Yun and Looney, Leslie W. and Stephens, Ian W. , title =. , year =. doi:10.1093/mnras/stv2633 , adsurl =

    work page doi:10.1093/mnras/stv2633

  71. [71]

    and Hoekstra, Alfons G

    Yurkin, Maxim A. and Hoekstra, Alfons G. , title =. JQSRT , year =. doi:10.1016/j.jqsrt.2011.01.031 , adsurl =

    work page doi:10.1016/j.jqsrt.2011.01.031 2011

  72. [72]

    and Facchini, S

    Zagaria, F. and Facchini, S. and Curone, P. and Williams, J. P. and Clarke, C. J. and Ribas, A. and Tazzari, M. and Mac. Multi-frequency analysis of the. , year =. doi:10.1051/0004-6361/202452986 , adsurl =

    work page doi:10.1051/0004-6361/202452986

  73. [73]

    and Zhu, Z

    Zhang, S. and Zhu, Z. and Ueda, T. and Kataoka, A. and Sierra, A. and Carrasco-Gonz. Porous Dust Particles in Protoplanetary Disks: Application to the HL Tau Disk , journal =. 2023 , volume =. doi:10.3847/1538-4357/acdb4e , adsurl =

    work page doi:10.3847/1538-4357/acdb4e 2023