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REVIEW 4 major objections 5 minor 74 references

Leaky dust trap in the PDS 70 disk revealed by ALMA Band 9 observations

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read ALMA's shortest submillimetre band sees PDS 70's dust ring peak 9 au inward of the longer-wavelength rings, an observational sign of small grains leaking from the dust trap.

desk verdict First resolved Band 9 map of PDS 70 shows a real inward peak shift, but the leaky-trap interpretation is one of two viable scenarios and the abstract overstates the confirmation. read the letter →

arxiv 2507.09402 v1 pith:6J7W6KTB submitted 2025-07-12 astro-ph.EP astro-ph.GA

Anibal Sierra , Myriam Benisty , Paola Pinilla , Laura Pérez , Pietro Curone , Kiyoaki Doi , Stefano Facchini , Daniele Fasano
show 8 more authors
Sean Andrews Jaehan Bae John Carpenter Ian Czekala Andrea Isella Nicolas Kurtovic Francois Menard Richard Teague
This is my paper · ORCID
classification astro-ph.EPastro-ph.GA
keywords protoplanetarydisksPDS70dusttrapsfiltrationpebblefluxALMABand9submillimetercontinuumplanet-diskinteraction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper presents new ALMA Band 9 (671 GHz, 447 $\mu$m) continuum observations of the planet-forming disk PDS 70 and uses them to test whether the disk's dust trap is completely sealed or leaks. The data show that the Band 9 ring peaks at 67.4 au, about 9 au closer to the star than the peak at longer millimeter wavelengths, with a tentative additional outer shoulder. If the brightness traces dust column density, this offset is the signature of small grains ($\sim 100\,\mu$m) escaping the pressure bump both inward and outward while larger grains remain trapped. Combined with multi-wavelength dust modeling and dust evolution simulations, the paper argues that a turbulent viscosity between roughly $\alpha = 10^{-3}$ and $5\times10^{-3}$ makes the PDS 70 dust trap leaky, feeding dust through the gap opened by the two planets. The result matters because it would be direct observational evidence for pebble flux across a planet-opened gap, a process that supplies inner disks and growing planets.

What carries the argument

The load-bearing mechanism is wavelength-dependent grain-size sensitivity combined with size-dependent dust diffusion. A dust trap is a local pressure maximum: large grains collect there, while small grains diffuse out through the dust diffusion coefficient $D \propto (\mathrm{St}^2+1)^{-1}$. Since ALMA Band 9 at 447 $\mu$m traces grains of order $\lambda/\pi \approx 140\,\mu$m, whereas Bands 7, 6, and 3 trace grains from roughly 0.27 mm to 0.95 mm, a radial offset between the 671 GHz ring peak and the longer-wavelength peaks is read as a radial gradient in the grain-size distribution. The argument is carried by visibility-based radial profile fitting, which recovers robust peak positions from each band's visibilities, and by dust evolution simulations that vary only the viscosity $\alpha$ ($1\times10^{-3}$, $2.5\times10^{-3}$, $5\times10^{-3}$) against a fixed PDS 70 gap shape, showing that intermediate $\alpha$ lets small grains escape while retaining large ones in the pressure bump.

What would settle it

A resolved Band 9 observation with baselines reaching roughly 1 M$\lambda$ (angular resolution well below 0.1 arcsec) that places the 671 GHz brightness peak at 0.68 arcsec rather than 0.60 arcsec, or a radiative-transfer fit showing that the Band 9 ring is optically thick once scattering opacity is included, would falsify the small-grain-filtration reading.

Watch

Extended reading notes

Core claim

New ALMA Band 9 observations of PDS 70 resolve the dust continuum ring at 671 GHz and show that its brightness peak sits at 0.60$^{\prime\prime}$ (67.4 au), clearly inward of the $\sim 0.68^{\prime\prime}$ (76.4 au) peak measured at 100--350 GHz and outward of the $\sim 54$ au infrared peak. The visibility modelling also reveals a tentative outer shoulder beyond the ring that is not seen at longer wavelengths. Because Band 9 is most sensitive to grains of size $a \sim \lambda/\pi \approx 140\,\mu$m (Stokes number $\sim 0.02$), and because small grains diffuse out of a pressure maximum more easily than large ones, the authors interpret the inward peak shift as radial segregation of dust by size: roughly 100 $\mu$m grains leak from the dust trap both inward, across the gap carved by PDS 70b and PDS 70c, and outward. Multi-wavelength spectral energy distribution modelling places the peak of dust surface density and centimetre-sized grains at the ring location, while the cavity grain size remains poorly constrained but is consistent with grains as small as 10 $\mu$m. Dust evolution models with viscosity $\alpha = 2.5\times10^{-3}$ reproduce a ring of trapped large grains together with small grains leaking through the gap, and the paper concludes that PDS 70's dust trap is leaky, validating theoretical dust filtration and confirming pebble flux through the gap.

Load-bearing premise

The conclusion turns the Band 9 brightness map into a dust-column-density map, which holds only under the paper's stated assumption that all observed wavelengths are optically thin and trace the same midplane temperature; if Band 9 is instead optically thick or emerges from warmer surface layers, the inward peak shift could be a temperature or optical-depth effect rather than small-grain leakage.

Editorial extensions

If this is right

  • If the inward leak is real, PDS 70's inner disk is continuously resupplied with small grains from the outer disk, explaining how the inner disk survives for millions of years despite the two giant planets.
  • The same observations imply that the gap cleared by PDS 70b and PDS 70c is not dust-empty; small grains crossing the gap can be accreted by the planets, affecting their growth and atmospheric composition.
  • Dust traps should not be treated as impermeable barriers: the amount of leakage is set by turbulence, with the models favouring $\alpha$ roughly between $10^{-3}$ and $5\times10^{-3}$.
  • The Band 9 outer shoulder, if confirmed at higher resolution, shows that grains also escape outward from the pressure bump, adding an outer leak and linking the shoulder to planet-driven outward gas flows.
  • The multi-wavelength fits place the dust surface density maximum and centimetre-sized grains at the ring, consistent with dust trap models, strengthening the general picture that pressure bumps hold large grains while leaking small ones.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the same peak-offset diagnostic could be applied to a sample of transition disks with confirmed embedded planets: if the leaky-trap picture is right, shorter-wavelength peaks should systematically lie inward of longer-wavelength peaks at comparable resolution, turning this single-object inference into a statistical test.
  • The favoured viscosity window is independently testable from gas kinematics: high-resolution CO line observations sensitive to turbulent broadening, or short-wavelength dust polarization, could measure turbulence without relying on the dust evolution model.
  • The paper's own caveat that scattering opacity might make Band 9 optically thick suggests a cleaner test: a radiative-transfer model that fits all bands with vertical temperature gradients and settled grains. If the Band 9 peak shift disappears once surface-layer emission is accounted for, the data constrain vertical disk structure rather than radial dust transport.
  • A targeted search for the Band 9 outer shoulder in scattered light or optically thin molecular emission at matched resolution could separate the shoulder's dust content from the main ring and directly test the outward-leak interpretation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper presents new ALMA Band 9 (671 GHz) continuum observations of the PDS 70 protoplanetary disk at 0.242 arcsec resolution. The data show a ring-like structure whose brightness peak lies at 0.60 arcsec (67.4 au), interior to the longer-wavelength peaks at ~0.68 arcsec (76.4 au) and exterior to the infrared peak at ~0.48 arcsec. The authors use Frankenstein visibility modelling to derive radial brightness profiles at multiple wavelengths, perform a multi-wavelength fit to constrain dust temperature, surface density, and maximum grain size, and present dust evolution models with different viscosity values. They conclude that the Band 9 peak traces small grains escaping the pressure bump both inward and outward, implying a leaky dust trap and pebble flux through the planet-opened gap, and they constrain the turbulent viscosity to roughly 1e-3 < alpha < 5e-3.

Significance. If the interpretation is correct, this would be one of the first direct observational indications of size-dependent dust segregation in a planet-carved gap, directly testing dust trapping and filtration models. The paper is strong on the observational side: it presents new ALMA Band 9 data, a careful self-calibration, visibility modelling with an exploration of hyper-parameter effects (Appendix A), and a resolution-matched consistency check that leaves a 60.5 mas peak offset (Section 5.1). The peak location at 0.60 arcsec is robust to the Frankenstein hyper-parameters. However, the physical interpretation is not unique because the paper itself raises an optically thick/temperature-gradient alternative (Section 5.1) that it does not quantitatively test, and the dust evolution models are compared only qualitatively to the observations. The contribution would be very valuable, but at present the central claim is not established to the standard expected for a strong journal.

major comments (4)
  1. [Sec. 5.1, 5.3] The central claim that the Band 9 peak traces dust column segregation rests on the assumption that all bands are optically thin and trace the same midplane temperature. In Section 5.3 the authors state that including scattering opacity shifts Band 9 (and also Bands 7 and 6) into the optically thick regime. In that regime, the observed brightness is set by the temperature at the tau~1 surface, not by the dust column. Since the fitted dust temperature decreases outward (Fig. 5), an optically thick Band 9 ring would peak interior to the column-density peak even for a single non-segregated dust population. The paper lists this as a 'possible scenario' but does not test it quantitatively. I request a calculation of the Band 9 intensity profile using the fitted T_d(r), Sigma_d(r), and scattering opacities to determine whether the observed 60.5 mas offset can be reproduced without invoking radial dust segregation. Without this test, the data do not uniquely demonstrate a leaky trap.
  2. [Sec. 4, Fig. 7] The dust evolution models are not quantitatively compared with the observations. The text states that 'reproducing in detail the fluxes and intensity radial profiles is beyond the scope of this work' and declares alpha = 2.5e-3 as the best case based on qualitative inspection. The conclusion that alpha ~ 2.5e-3 is therefore a proof of concept, not a constraint. Please compute synthetic Band 7 and Band 9 intensity profiles from the modeled dust surface density distributions (with appropriate opacities and temperatures) and compare the predicted peak locations with the observed 0.60 arcsec and 0.68 arcsec peaks. A quantitative goodness-of-fit metric would turn the 'best' choice into a falsifiable test and would also clarify whether the model actually produces a 9 au shift.
  3. [Sec. 3.2, 5.1] The significance of the peak offset is not quantified. The Band 9 effective resolution derived from the visibility modelling is 176.5 mas, and the resolution-matched offset is 60.5 mas. The paper quotes the Band 9 peak at 0.60 arcsec without an uncertainty. Please provide an uncertainty on the peak location (e.g., from the Frankenstein posterior or bootstrap resampling of the visibilities) and state the significance of the offset relative to the longer-wavelength peaks. This is load-bearing for the main claim, because an offset smaller than the effective resolution may still be significant if the centroid is well constrained, but the paper currently gives no error bars.
  4. [Sec. 5.2, Conclusions] The outer shoulder is the only evidence for outward escape, but Appendix A shows it appears only for ws <= 1e-3 and for some alpha_f values, and Section 5.2 calls it tentative. The final conclusions (bullet 5) nevertheless state that small grains escape 'both inwards and outwards' as if this were established. Please either soften the conclusion to reflect the tentative nature of the shoulder, or provide additional support (e.g., detection in an independent data set or a robustness test that quantifies the significance of the shoulder).
minor comments (5)
  1. [Sec. 3.3, Eq. (1)] The weight for Band 9 is set to 2 in the chi-squared definition 'to provide a stronger constraint on the disc temperature'. This choice is not justified quantitatively; please discuss its effect on the inferred T_d(r) profile.
  2. [Figure 4 caption] The caption says 'at an angular resolution of 242\'\''; this should be 0.242 arcsec (or 242 mas).
  3. [Throughout] The name of the star is written inconsistently as 'PDS70' and 'PDS 70'; please unify to 'PDS 70'.
  4. [Sec. 5.3] The sentence comparing the Band 9 major-axis asymmetry to 'Figure 1 in Facchini et al. (2021)' would be clearer if the comparison image were included or described in more detail.
  5. [Appendix C, Fig. C2] The high-resolution model 'fails to reproduce the width of the ring and the position of the peak' but reproduces the amplitude; this important caveat should be stated in the main text near the multi-wavelength fit discussion.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Band 9 peak-shift measurement, SED modeling, and dust evolution simulations form an independent derivation chain; the flagged temperature/optical-depth degeneracy is an alternative interpretation, not a circular reduction.

full rationale

The central observational claim is a direct visibility-space measurement: Band 9 peaks at 0.60'' while longer-wavelength bands peak at 0.68'', and Frankenstein fits at different hyper-parameters keep the peak at 0.60'' (Appendix A). The multi-wavelength SED analysis is a forward radiative-transfer fit using DSHARP opacities; it is not calibrated to force the Band 9 peak shift, and the high-resolution fit explicitly excludes Band 9, using the low-resolution Band 9 temperature only as a prior (Eq. 2, Section 3.3). Appendix C shows that this high-resolution model does not reproduce the Band 9 morphology, so the Band 9 data are not used to manufacture the predicted Band 9 profile. The dust evolution models are new calculations seeded by Pinilla et al. (2024) with changed alpha values; the simulations are not fitted to the Band 9 images, and the statement that alpha = 2.5e-3 is 'the best one explaining the observations' is a qualitative model selection, not a fitted output renamed as a prediction. The only self-citation to Pinilla et al. (2024) sets model parameters and framing; it does not by itself force the leaky-trap conclusion. Finally, Section 5.1 explicitly states the load-bearing assumption that all wavelengths trace the same midplane temperature and are optically thin, and Section 5.3 acknowledges that scattering opacity can shift Band 9 into the optically thick regime, where the brightness peak is set by temperature rather than dust column. This is a real alternative interpretation and a limitation, but it is not circularity: the observed peak offset is not definitionally equivalent to the conclusion, and the paper does not fit its input data so that the conclusion is true by construction.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The central interpretation stacks several assumptions: optically thin isothermal emission, a one-to-one wavelength-to-grain-size mapping through DSHARP opacities, and a specific planet-driven gap model in the dust evolution code. All are standard in the field and are stated, but none is independently verified here, and the alpha constraint is qualitative rather than a measured value.

free parameters (8)
  • Band 9 chi-squared weight w_nu = 2
    Chosen by hand to give Band 9 a stronger constraint on temperature in the low-resolution multi-wavelength fit (Section 3.3); affects the fitted T_d and the temperature prior used in the high-resolution fit.
  • Frankenstein smoothness hyper-parameter w_s (Band 9) = 1e-4
    Chosen to fit the power spectrum at the longest baselines; the outer and inner shoulders appear only for w_s <= 1e-3 (Appendix A), so the shoulder detection depends on this choice.
  • Frankenstein SNR threshold alpha_f = 1.3
    Chosen as a conservative SNR threshold; Appendix A shows the shoulders are not recovered for higher alpha_f.
  • Dust temperature T_d(r) = Radial profile, about 20-30 K at the ring
    Free parameter per radial bin in the SED fit (Section 3.3).
  • Dust surface density Sigma_d(r) = Radial profile, peak about 1e-2 g cm^-2
    Free parameter per radial bin; the inferred total dust mass depends on the assumed grain size distribution slope p.
  • Maximum grain size a_max(r) = Radial profile, about 1 cm in the ring and lower beyond 100 au
    Free parameter per radial bin; inside the gap it is unconstrained, spanning roughly 10 micron to 1 cm at 2 sigma.
  • Grain size distribution slope p = 2.5, 3.0, 3.5 (grid)
    Not fitted; three values are explored, with p=3.0 preferred for matching the infrared slope. The inferred a_max and Sigma_d depend on p.
  • Disk viscosity alpha in dust evolution models = 1e-3, 2.5e-3, 5e-3
    Varying alpha is the lever used to explain the peak shift; alpha=2.5e-3 is declared best after comparing with observations (Section 4).
assumptions (6)
  • domain assumption All observed bands are optically thin and trace the same midplane temperature
    Section 5.1 states this assumption explicitly: 'we assume that all wavelengths are sensitive to the same temperature, and most of their emission and optical depth come from the midplane.' The peak-shift interpretation as dust mass segregation depends on it.
  • domain assumption DSHARP opacities with sensitivity peaking at a_max ~ lambda/pi
    Section 5.1 maps Bands 9, 7, 6, and 3 to grain sizes of 0.14, 0.27, 0.43, and 0.95 mm respectively; this wavelength-to-grain-size mapping anchors the dust segregation argument.
  • domain assumption Grain size distribution n(a) da proportional to a^-p da with a_min = 0.5 micron
    Section 3.3: used in the SED fitting; a_min is fixed and p is scanned over three values.
  • domain assumption Disk geometry (inclination 51.7 deg, PA 160.4 deg) from Benisty et al. 2021 and axisymmetry after arc subtraction
    Used for radial profiles and Frankenstein fits (Sections 3.1 and 3.2).
  • domain assumption Dust evolution model parameters from Pinilla et al. (2024), including planet masses 2.5 and 5 MJup from Bae et al. (2019), fragmentation velocity 10 m/s, and initial grain sizes 0.01-1 micron
    Section 4: the alpha conclusion is conditional on these model inputs; no variation of planet masses or fragmentation velocity is explored.
  • domain assumption The azimuthal asymmetry subtraction correctly isolates the axisymmetric ring
    Section 3.2: the arc mask from Benisty et al. (2021) is applied before visibility modelling; errors in the mask propagate to the reconstructed radial profile.

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Cite this review

Pith. "Pith review of Leaky dust trap in the PDS 70 disk revealed by ALMA Band 9 observations." pith.science (2026). https://pith.science/paper/6J7W6KTB

@misc{pith2026250709402,
  author       = {Pith},
  title        = {Pith review of: Leaky dust trap in the PDS 70 disk revealed by ALMA Band 9 observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6J7W6KTB}},
  note         = {Machine review of arXiv:2507.09402}
}
abstract

We present new observations of the PDS 70 disc obtained with the Atacama Large Millimeter/sub-millimeter Array (ALMA) in Band 9 (671 GHz) at 0.242$^{\prime\prime}$ resolution, which provide valuable insights into the spatial distribution of sub-millimetre grains in the disc. The data reveal a ring-like morphology, with a radial peak located between those previously observed at infrared wavelengths and longer millimetre observations. Additionally, we detect a tentative outer shoulder in Band 9 that is not observed at longer wavelengths. These findings suggest that small grains ($\sim 100 \mu$m) traced by Band 9 may be escaping from the pressure bump both radially inwards and outwards, or may be tracing different disc layers than those probed at longer wavelengths. A multi-wavelength analysis of the disc at millimetre wavelengths and the best fit to the spectral energy distribution shows the presence of centimetre grains around the ring location, where the dust surface density also peaks, compatible with dust trap models. The grain size in the disc cavity is not well constrained but is consistent with grains as small as 10 $\mu$m, supporting the hypothesis that small dust grain filters through the cavity. We use dust evolution models to demonstrate that a turbulent viscosity of $\alpha \gtrsim 10^{-3}$ allows small grains to filter through the disc gap, while $\alpha \lesssim 5 \times 10^{-3}$ is required to retain large grains in the pressure bump. The Band 9 observations of PDS 70 validate theoretical models and confirm the presence of pebble flux through the disc gap.

Figures

Figures reproduced from arXiv: 2507.09402 by the authors.

Figure 1
Figure 1. Left: Dust continuum image at ALMA Band 9 (671 GHz). Middle: Azimuthal profile around the ring. The arrows indicate the azimuth of the northwest and southeast major axes. Right: Brightness temperature radial profile of PDS 70 extracted from the ALMA images at different wavelengths: 100 GHz (red), 220 GHz (yellow), 260 GHz (green), 350 GHz (blue), 671 GHz (purple). The horizontal lines show the angular resolution for… view at source ↗
Figure 2
Figure 2. Visibility modelling of the disc around PDS 70 at different wavelengths. Left: tclean image of the dust continuum data. Middle left: tclean image of the symmetric dust continuum data. Middle right: tclean image of the Frankenstein model. Right: tclean map of the residual visibilities (Symmetric - Model). The white iso-contour show the region with residuals above/below ±5𝜎. The units of all colour bars are mJy beam−1… view at source ↗
Figure 3
Figure 3. Left: Radial profiles of the brightness temperature obtained from the visibility fit at different ALMA wavelengths (see colour code). The vertical dashed-dotted lines indicate the orbits of PDS 70b, and PDS 70c. Right: Zoom-in around the ring peaks. The grey dashed line shows the normalised brightness radial profile from infrared observations at H band (𝜆 = 1.625𝜇m). The radial positions of the peaks are shown as ve… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: shows the spectral index radial profile between different bands computed from the intensity profiles in the image plane at a common angular resolution of 0.242′′. The central emission of the disc (around one beam size) is contaminated by free-free emission at Band 3 (D…
Figure 5
Figure 5. Figure 5: Dust properties constraints inferred from multi-wavelength analysis for different slopes of the particle size distribution 𝑝 . Left: Dust temperature. Middle: Dust surface density. Right: Maximum grain size. The angular resolution is indicated in the bottom left corner…
Figure 6
Figure 6. Figure 6: Optical depth radial profiles from the dust continuum multi￾wavelength modelling (see colour code). The angular resolution for each band is indicated in the bottom-left corner. The dashed vertical lines show the position of the peak at Band 9 and Band 7. 4 LEAKINESS OF…
Figure 7
Figure 7. Figure 7: Dust segregation models for the disc around PDS 70. Different coloured lines (see colour code) show the dust surface density distribution for different grain sizes. The turbulent viscosity parameters in each simulation are 𝛼 = 1 × 10−3 , 2.5 × 10−3 , 5 × 10−3 from left…

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Works this paper leans on

74 extracted references · 5 canonical work pages

  1. [1]

    M., et al., 2018, @doi [ ] 10.3847/2041-8213/aaf741 , https://ui.adsabs.harvard.edu/abs/2018ApJ...869L..41A 869, L41

    Andrews S. M., et al., 2018, @doi [ ] 10.3847/2041-8213/aaf741 , https://ui.adsabs.harvard.edu/abs/2018ApJ...869L..41A 869, L41

    doi:10.3847/2041-8213/aaf741 2018

  2. [2]

    M., et al., 2021, @doi [ ] 10.3847/1538-4357/ac00b9 , https://ui.adsabs.harvard.edu/abs/2021ApJ...916...51A 916, 51

    Andrews S. M., et al., 2021, @doi [ ] 10.3847/1538-4357/ac00b9 , https://ui.adsabs.harvard.edu/abs/2021ApJ...916...51A 916, 51

    doi:10.3847/1538-4357/ac00b9 2021

  3. [3]

    Astropy Collaboration et al., 2013, @doi [ ] 10.1051/0004-6361/201322068 , http://adsabs.harvard.edu/abs/2013A

    doi:10.1051/0004-6361/201322068 2013

  4. [4]

    Astropy Collaboration et al., 2018, @doi [ ] 10.3847/1538-3881/aabc4f , https://ui.adsabs.harvard.edu/abs/2018AJ....156..123A 156, 123

    doi:10.3847/1538-3881/aabc4f 2018

  5. [5]

    Bae J., et al., 2019, @doi [ ] 10.3847/2041-8213/ab46b0 , https://ui.adsabs.harvard.edu/abs/2019ApJ...884L..41B 884, L41

    doi:10.3847/2041-8213/ab46b0 2019

  6. [6]

    Benisty M., et al., 2021, @doi [ ] 10.3847/2041-8213/ac0f83 , https://ui.adsabs.harvard.edu/abs/2021ApJ...916L...2B 916, L2

    doi:10.3847/2041-8213/ac0f83 2021

  7. [7]

    Bi J., Lin M.-K., 2024, @doi [ ] 10.3847/1538-4357/ad5be2 , https://ui.adsabs.harvard.edu/abs/2024ApJ...971...76B 971, 76

    doi:10.3847/1538-4357/ad5be2 2024

  8. [8]

    M., Ercolano B., 2012, @doi [ ] 10.1051/0004-6361/201219262 , https://ui.adsabs.harvard.edu/abs/2012A&A...544A..79B 544, A79

    Birnstiel T., Andrews S. M., Ercolano B., 2012, @doi [ ] 10.1051/0004-6361/201219262 , https://ui.adsabs.harvard.edu/abs/2012A&A...544A..79B 544, A79

    doi:10.1051/0004-6361/201219262 2012

Show all 74 references
  1. [9]

    P., Pinilla P., 2013, @doi [ ] 10.1051/0004-6361/201220847 , https://ui.adsabs.harvard.edu/abs/2013A&A...550L...8B 550, L8

    Birnstiel T., Dullemond C. P., Pinilla P., 2013, @doi [ ] 10.1051/0004-6361/201220847 , https://ui.adsabs.harvard.edu/abs/2013A&A...550L...8B 550, L8

    2013 doi

  2. [10]

    Birnstiel T., et al., 2018, @doi [ ] 10.3847/2041-8213/aaf743 , https://ui.adsabs.harvard.edu/abs/2018ApJ...869L..45B 869, L45

    2018 doi

  3. [11]

    Blum J., Wurm G., 2008, @doi [ ] 10.1146/annurev.astro.46.060407.145152 , https://ui.adsabs.harvard.edu/abs/2008ARA&A..46...21B 46, 21

    2008

  4. [12]

    CASA Team et al., 2022, @doi [ ] 10.1088/1538-3873/ac9642 , https://ui.adsabs.harvard.edu/abs/2022PASP..134k4501C 134, 114501

    2022 doi

  5. [13]

    M., Esplin T

    Carpenter J. M., Esplin T. L., Luhman K. L., Mamajek E. E., Andrews S. M., 2025, @doi [ ] 10.3847/1538-4357/ad8ebc , https://ui.adsabs.harvard.edu/abs/2025ApJ...978..117C 978, 117

    2025 doi

  6. [14]

    Carrasco-Gonz \'a lez C., et al., 2019, @doi [ ] 10.3847/1538-4357/ab3d33 , https://ui.adsabs.harvard.edu/abs/2019ApJ...883...71C 883, 71

    2019 doi

  7. [15]

    A., et al., 2019, @doi [ ] 10.1093/mnras/sty2653 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.482..698C 482, 698

    Cieza L. A., et al., 2019, @doi [ ] 10.1093/mnras/sty2653 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.482..698C 482, 698

    2019 doi

  8. [16]

    J., 2008, @doi [IEEE Journal of Selected Topics in Signal Processing] 10.1109/JSTSP.2008.2006388 , https://ui.adsabs.harvard.edu/abs/2008ISTSP...2..793C 2, 793

    Cornwell T. J., 2008, @doi [IEEE Journal of Selected Topics in Signal Processing] 10.1109/JSTSP.2008.2006388 , https://ui.adsabs.harvard.edu/abs/2008ISTSP...2..793C 2, 793

    2008

  9. [17]

    Doi K., Kataoka A., 2021, @doi [ ] 10.3847/1538-4357/abe5a6 , https://ui.adsabs.harvard.edu/abs/2021ApJ...912..164D 912, 164

    2021 doi

  10. [18]

    B., Yoshida T

    Doi K., Kataoka A., Liu H. B., Yoshida T. C., Benisty M., Dong R., Yamato Y., Hashimoto J., 2024, @doi [ ] 10.3847/2041-8213/ad7f51 , https://ui.adsabs.harvard.edu/abs/2024ApJ...974L..25D 974, L25

    2024 doi

  11. [19]

    N., Wurm G., 2007, in Reipurth B., Jewitt D., Keil K., eds, Protostars and Planets V

    Dominik C., Blum J., Cuzzi J. N., Wurm G., 2007, in Reipurth B., Jewitt D., Keil K., eds, Protostars and Planets V. p. 783 ( @eprint arXiv astro-ph/0602617 ), @doi 10.48550/arXiv.astro-ph/0602617

    2007 doi arXiv

  12. [20]

    Dong R., et al., 2012, @doi [ ] 10.1088/0004-637X/760/2/111 , https://ui.adsabs.harvard.edu/abs/2012ApJ...760..111D 760, 111

    2012 doi

  13. [21]

    T., 2006, @doi [ ] 10.1086/498130 , https://ui.adsabs.harvard.edu/abs/2006ApJ...636.1114D 636, 1114

    Draine B. T., 2006, @doi [ ] 10.1086/498130 , https://ui.adsabs.harvard.edu/abs/2006ApJ...636.1114D 636, 1114

    2006 doi

  14. [22]

    M., Li H., 2019, @doi [ ] 10.3847/1538-4357/ab46b7 , https://ui.adsabs.harvard.edu/abs/2019ApJ...885...91D 885, 91

    Dra \.z kowska J., Li S., Birnstiel T., Stammler S. M., Li H., 2019, @doi [ ] 10.3847/1538-4357/ab46b7 , https://ui.adsabs.harvard.edu/abs/2019ApJ...885...91D 885, 91

    2019 doi

  15. [23]

    J., Klahr H., Henning T., 2010, @doi [ ] 10.1051/0004-6361/200912834 , https://ui.adsabs.harvard.edu/abs/2010A&A...515A..70D 515, A70

    Dzyurkevich N., Flock M., Turner N. J., Klahr H., Henning T., 2010, @doi [ ] 10.1051/0004-6361/200912834 , https://ui.adsabs.harvard.edu/abs/2010A&A...515A..70D 515, A70

    2010 doi

  16. [24]

    Facchini S., Teague R., Bae J., Benisty M., Keppler M., Isella A., 2021, @doi [ ] 10.3847/1538-3881/abf0a4 , https://ui.adsabs.harvard.edu/abs/2021AJ....162...99F 162, 99

    2021 doi

  17. [25]

    P., Dzyurkevich N., Henning T., Klahr H., Wolf S., 2015, @doi [ ] 10.1051/0004-6361/201424693 , https://ui.adsabs.harvard.edu/abs/2015A&A...574A..68F 574, A68

    Flock M., Ruge J. P., Dzyurkevich N., Henning T., Klahr H., Wolf S., 2015, @doi [ ] 10.1051/0004-6361/201424693 , https://ui.adsabs.harvard.edu/abs/2015A&A...574A..68F 574, A68

    2015 doi

  18. [26]

    W., Lang D., Goodman J., 2013, @doi [ ] 10.1086/670067 , https://ui.adsabs.harvard.edu/abs/2013PASP..125..306F 125, 306

    Foreman-Mackey D., Hogg D. W., Lang D., Goodman J., 2013, @doi [ ] 10.1086/670067 , https://ui.adsabs.harvard.edu/abs/2013PASP..125..306F 125, 306

    2013 doi

  19. [27]

    F., Laibe G., Maddison S

    Gonzalez J. F., Laibe G., Maddison S. T., 2017, @doi [ ] 10.1093/mnras/stx016 , https://ui.adsabs.harvard.edu/abs/2017MNRAS.467.1984G 467, 1984

    2017 doi

  20. [28]

    R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    Harris C. R., et al., 2020, @doi [Nature] 10.1038/s41586-020-2649-2 , 585, 357

    2020 doi

  21. [29]

    Huang J., et al., 2020, @doi [ ] 10.3847/1538-4357/ab711e , https://ui.adsabs.harvard.edu/abs/2020ApJ...891...48H 891, 48

    2020 doi

  22. [30]

    J., Dong R., Bai X.-N., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2503.19026 , https://ui.adsabs.harvard.edu/abs/2025arXiv250319026H p

    Huang P., Yu F., Lee E. J., Dong R., Bai X.-N., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2503.19026 , https://ui.adsabs.harvard.edu/abs/2025arXiv250319026H p. arXiv:2503.19026

    2025 doi arXiv

  23. [31]

    D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    Hunter J. D., 2007, @doi [Computing in Science & Engineering] 10.1109/MCSE.2007.55 , 9, 90

    2007 doi

  24. [32]

    Isella A., Benisty M., Teague R., Bae J., Keppler M., Facchini S., P \'e rez L., 2019, @doi [ ] 10.3847/2041-8213/ab2a12 , https://ui.adsabs.harvard.edu/abs/2019ApJ...879L..25I 879, L25

    2019 doi

  25. [33]

    A., Tazzari M., Rosotti G

    Jennings J., Booth R. A., Tazzari M., Rosotti G. P., Clarke C. J., 2020, @doi [ ] 10.1093/mnras/staa1365 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.495.3209J 495, 3209

    2020 doi

  26. [34]

    A., Tazzari M., Clarke C

    Jennings J., Booth R. A., Tazzari M., Clarke C. J., Rosotti G. P., 2022, @doi [ ] 10.1093/mnras/stab3185 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.509.2780J 509, 2780

    2022 doi

  27. [35]

    Johansen A., Youdin A., Klahr H., 2009, @doi [ ] 10.1088/0004-637X/697/2/1269 , https://ui.adsabs.harvard.edu/abs/2009ApJ...697.1269J 697, 1269

    2009 doi

  28. [36]

    Keppler M., et al., 2018, @doi [ ] 10.1051/0004-6361/201832957 , https://ui.adsabs.harvard.edu/abs/2018A&A...617A..44K 617, A44

    2018 doi

  29. [37]

    J., et al., 2024, @doi [ ] 10.3847/1538-4357/ad24d2 , https://ui.adsabs.harvard.edu/abs/2024ApJ...964..190L 964, 190

    Law C. J., et al., 2024, @doi [ ] 10.3847/1538-4357/ad24d2 , https://ui.adsabs.harvard.edu/abs/2024ApJ...964..190L 964, 190

    2024 doi

  30. [38]

    W., Fromang S., 2014, @doi [ ] 10.1051/0004-6361/201423660 , https://ui.adsabs.harvard.edu/abs/2014A&A...566A..56L 566, A56

    Lesur G., Kunz M. W., Fromang S., 2014, @doi [ ] 10.1051/0004-6361/201423660 , https://ui.adsabs.harvard.edu/abs/2014A&A...566A..56L 566, A56

    2014 doi

  31. [39]

    C., et al., 2018, @doi [ ] 10.3847/1538-4357/aaba7c , https://ui.adsabs.harvard.edu/abs/2018ApJ...858..112L 858, 112

    Long Z. C., et al., 2018, @doi [ ] 10.3847/1538-4357/aaba7c , https://ui.adsabs.harvard.edu/abs/2018ApJ...858..112L 858, 112

    2018 doi

  32. [40]

    C., Huang J., Andrews S

    Mac \' as E., Guerra-Alvarado O., Carrasco-Gonz \'a lez C., Ribas \'A ., Espaillat C. C., Huang J., Andrews S. M., 2021, @doi [ ] 10.1051/0004-6361/202039812 , https://ui.adsabs.harvard.edu/abs/2021A&A...648A..33M 648, A33

    2021 doi

  33. [41]

    P., Waters B., Schiebel D., Young W., Golap K., 2007, in Shaw R

    McMullin J. P., Waters B., Schiebel D., Young W., Golap K., 2007, in Shaw R. A., Hill F., Bell D. J., eds, Astronomical Society of the Pacific Conference Series Vol. 376, Astronomical Data Analysis Software and Systems XVI. p. 127

    2007

  34. [42]

    Mesa D., et al., 2019, @doi [ ] 10.1051/0004-6361/201936764 , https://ui.adsabs.harvard.edu/abs/2019A&A...632A..25M 632, A25

    2019 doi

  35. [43]

    M \"u ller A., et al., 2018, @doi [ ] 10.1051/0004-6361/201833584 , https://ui.adsabs.harvard.edu/abs/2018A&A...617L...2M 617, L2

    2018 doi

  36. [44]

    J., Mellema G., 2006, @doi [ ] 10.1051/0004-6361:20054449 , https://ui.adsabs.harvard.edu/abs/2006A&A...453.1129P 453, 1129

    Paardekooper S. J., Mellema G., 2006, @doi [ ] 10.1051/0004-6361:20054449 , https://ui.adsabs.harvard.edu/abs/2006A&A...453.1129P 453, 1129

    2006 doi

  37. [45]

    Perotti G., et al., 2023, @doi [ ] 10.1038/s41586-023-06317-9 , https://ui.adsabs.harvard.edu/abs/2023Natur.620..516P 620, 516

    2023 doi

  38. [46]

    P., Uribe A

    Pinilla P., Birnstiel T., Ricci L., Dullemond C. P., Uribe A. L., Testi L., Natta A., 2012a, @doi [ ] 10.1051/0004-6361/201118204 , https://ui.adsabs.harvard.edu/abs/2012A&A...538A.114P 538, A114

    doi

  39. [47]

    Pinilla P., Benisty M., Birnstiel T., 2012b, @doi [ ] 10.1051/0004-6361/201219315 , https://ui.adsabs.harvard.edu/abs/2012A&A...545A..81P 545, A81

    doi

  40. [48]

    P., 2016, @doi [ ] 10.1051/0004-6361/201527131 , https://ui.adsabs.harvard.edu/abs/2016A&A...585A..35P 585, A35

    Pinilla P., Klarmann L., Birnstiel T., Benisty M., Dominik C., Dullemond C. P., 2016, @doi [ ] 10.1051/0004-6361/201527131 , https://ui.adsabs.harvard.edu/abs/2016A&A...585A..35P 585, A35

    2016 doi

  41. [49]

    Pinilla P., Benisty M., Waters R., Bae J., Facchini S., 2024, @doi [ ] 10.1051/0004-6361/202348707 , https://ui.adsabs.harvard.edu/abs/2024A&A...686A.135P 686, A135

    2024 doi

  42. [50]

    Rampinelli L., et al., 2024, @doi [ ] 10.1051/0004-6361/202449698 , https://ui.adsabs.harvard.edu/abs/2024A&A...689A..65R 689, A65

    2024 doi

  43. [51]

    J., 2010, @doi [ ] 10.1051/0004-6361/200913403 , https://ui.adsabs.harvard.edu/abs/2010A&A...512A..15R 512, A15

    Ricci L., Testi L., Natta A., Neri R., Cabrit S., Herczeg G. J., 2010, @doi [ ] 10.1051/0004-6361/200913403 , https://ui.adsabs.harvard.edu/abs/2010A&A...512A..15R 512, A15

    2010 doi

  44. [52]

    Rice W. K. M., Armitage P. J., Wood K., Lodato G., 2006, @doi [ ] 10.1111/j.1365-2966.2006.11113.x , https://ui.adsabs.harvard.edu/abs/2006MNRAS.373.1619R 373, 1619

    2006

  45. [53]

    Sierra A., Lizano S., 2020, @doi [ ] 10.3847/1538-4357/ab7d32 , https://ui.adsabs.harvard.edu/abs/2020ApJ...892..136S 892, 136

    2020 doi

  46. [54]

    Sierra A., et al., 2021, @doi [ ] 10.3847/1538-4365/ac1431 , https://ui.adsabs.harvard.edu/abs/2021ApJS..257...14S 257, 14

    2021 doi

  47. [55]

    Sierra A., et al., 2024, @doi [ ] 10.3847/1538-4357/ad7460 , https://ui.adsabs.harvard.edu/abs/2024ApJ...974..306S 974, 306

    2024 doi

  48. [56]

    M., Lichtenberg T., Dr a \.z kowska J., Birnstiel T., 2023, @doi [ ] 10.1051/0004-6361/202245512 , https://ui.adsabs.harvard.edu/abs/2023A&A...670L...5S 670, L5

    Stammler S. M., Lichtenberg T., Dr a \.z kowska J., Birnstiel T., 2023, @doi [ ] 10.1051/0004-6361/202245512 , https://ui.adsabs.harvard.edu/abs/2023A&A...670L...5S 670, L5

    2023 doi

  49. [57]

    G., 1851, Transactions of the Cambridge Philosophical Society, https://ui.adsabs.harvard.edu/abs/1851TCaPS...9....8S 9, 8

    Stokes G. G., 1851, Transactions of the Cambridge Philosophical Society, https://ui.adsabs.harvard.edu/abs/1851TCaPS...9....8S 9, 8

  50. [58]

    Takeuchi T., Lin D. N. C., 2002, @doi [ ] 10.1086/344437 , https://ui.adsabs.harvard.edu/abs/2002ApJ...581.1344T 581, 1344

    2002 doi

  51. [59]

    Tazzari M., Beaujean F., Testi L., 2018, @doi [ ] 10.1093/mnras/sty409 , http://adsabs.harvard.edu/abs/2018MNRAS.476.4527T 476, 4527

    2018 doi

  52. [60]

    A., 2019, @doi [ ] 10.3847/2041-8213/ab4a83 , https://ui.adsabs.harvard.edu/abs/2019ApJ...884L..56T 884, L56

    Teague R., Bae J., Huang J., Bergin E. A., 2019, @doi [ ] 10.3847/2041-8213/ab4a83 , https://ui.adsabs.harvard.edu/abs/2019ApJ...884L..56T 884, L56

    2019 doi

  53. [61]

    R., Moran J

    Thompson A. R., Moran J. M., Swenson George W. J., 2017, Interferometry and Synthesis in Radio Astronomy, 3rd Edition , @doi 10.1007/978-3-319-44431-4

    2017 doi

  54. [62]

    J., Testi L., 2020, @doi [ ] 10.1093/mnras/staa2933 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.499.2015T 499, 2015

    Toci C., Lodato G., Christiaens V., Fedele D., Pinte C., Price D. J., Testi L., 2020, @doi [ ] 10.1093/mnras/staa2933 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.499.2015T 499, 2015

    2020 doi

  55. [63]

    Viscardi E. M., Mac \' as E., Zagaria F., Sierra A., Jiang H., Yoshida T., Curone P., 2025, @doi [arXiv e-prints] 10.48550/arXiv.2501.13877 , https://ui.adsabs.harvard.edu/abs/2025arXiv250113877V p. arXiv:2501.13877

    2025 doi arXiv

  56. [64]

    Wahhaj Z., et al., 2024, @doi [ ] 10.1051/0004-6361/202349018 , https://ui.adsabs.harvard.edu/abs/2024A&A...687A.257W 687, A257

    2024 doi

  57. [65]

    J., et al., 2021, @doi [ ] 10.3847/1538-3881/abdb2d , https://ui.adsabs.harvard.edu/abs/2021AJ....161..148W 161, 148

    Wang J. J., et al., 2021, @doi [ ] 10.3847/1538-3881/abdb2d , https://ui.adsabs.harvard.edu/abs/2021AJ....161..148W 161, 148

    2021 doi

  58. [66]

    J., 1977, @doi [ ] 10.1093/mnras/180.2.57 , https://ui.adsabs.harvard.edu/abs/1977MNRAS.180...57W 180, 57

    Weidenschilling S. J., 1977, @doi [ ] 10.1093/mnras/180.2.57 , https://ui.adsabs.harvard.edu/abs/1977MNRAS.180...57W 180, 57

    1977 doi

  59. [67]

    L., 1972, in Elvius A., ed., From Plasma to Planet

    Whipple F. L., 1972, in Elvius A., ed., From Plasma to Planet. p. 211

    1972

  60. [68]

    A., Hartmann L., 1992, @doi [ ] 10.1086/171673 , https://ui.adsabs.harvard.edu/abs/1992ApJ...395..529W 395, 529

    Whitney B. A., Hartmann L., 1992, @doi [ ] 10.1086/171673 , https://ui.adsabs.harvard.edu/abs/1992ApJ...395..529W 395, 529

    1992 doi

  61. [69]

    N., Lithwick Y., 2007, @doi [ ] 10.1016/j.icarus.2007.07.012 , https://ui.adsabs.harvard.edu/abs/2007Icar..192..588Y 192, 588

    Youdin A. N., Lithwick Y., 2007, @doi [ ] 10.1016/j.icarus.2007.07.012 , https://ui.adsabs.harvard.edu/abs/2007Icar..192..588Y 192, 588

    2007 doi

  62. [70]

    Zhou Y., et al., 2025, @doi [ ] 10.3847/2041-8213/adb134 , https://ui.adsabs.harvard.edu/abs/2025ApJ...980L..39Z 980, L39

    2025 doi

  63. [71]

    P., Dong R., Espaillat C., Hartmann L., 2012, @doi [ ] 10.1088/0004-637X/755/1/6 , https://ui.adsabs.harvard.edu/abs/2012ApJ...755....6Z 755, 6

    Zhu Z., Nelson R. P., Dong R., Espaillat C., Hartmann L., 2012, @doi [ ] 10.1088/0004-637X/755/1/6 , https://ui.adsabs.harvard.edu/abs/2012ApJ...755....6Z 755, 6

    2012 doi

  64. [72]

    de Juan Ovelar M., Min M., Dominik C., Thalmann C., Pinilla P., Benisty M., Birnstiel T., 2013, @doi [ ] 10.1051/0004-6361/201322218 , https://ui.adsabs.harvard.edu/abs/2013A&A...560A.111D 560, A111

    2013 doi

  65. [73]

    de Juan Ovelar M., Pinilla P., Min M., Dominik C., Birnstiel T., 2016, @doi [ ] 10.1093/mnrasl/slw051 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.459L..85D 459, L85

    2016 doi

  66. [74]

    write newline

    " write newline "" before.all 'output.state := FUNCTION fin.entry write newline FUNCTION new.block output.state before.all = 'skip after.block 'output.state := if FUNCTION new.sentence output.state after.block = 'skip output.state before.all = 'skip after.sentence 'output.stat...

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.