Pith. sign in

REVIEW 6 minor 85 references

The effect of radiation pressure on the dispersal of photoevaporating discs

T0 review · 0 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Radiation pressure cannot solve the relic disc problem: dust outflows remove material 5–10 times too slowly.

desk verdict The definitive 2D test shows radiation pressure does not solve the relic disc problem, and the negative result is robust and likely conservative. read the letter →

arxiv 2412.05054 v1 pith:YVOJZLO3 submitted 2024-12-06 astro-ph.EP

Alfie Robinson , James E. Owen , Richard A. Booth This is my paper · ORCID
classification astro-ph.EP
keywords protoplanetarydiscsphotoevaporationradiationpressuredustgrowthandfragmentationtransitionrelicradiativetransfermassloss
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

Photoevaporation models predict that many discs should linger as non-accreting transition discs with large dusty cavities, but such 'relic discs' are rarely observed. This paper asks whether radiation pressure from the central star can disperse the remaining dust quickly enough to resolve that mismatch, using global 2D simulations that track dust growth, fragmentation, radiative transfer, and photoevaporative winds. The simulations find that dust mass-loss rates from the inner rim of the outer disc are typically 5–10 times too small to keep pace with refilling of the dust trap, because grains larger than about a micron are launched outward but fall back into the disc. Only discs with smooth, EUV-like wind profiles, gas mass-loss rates above about $5\times10^{-9}\,M_\odot\,\mathrm{yr}^{-1}$, and less than about $1\,M_\oplus$ of dust at gap opening clear within the observed timescales. The paper concludes that radiation pressure is not the missing dispersal mechanism in current photoevaporation models.

What carries the argument

The load-bearing element is the balance of forces on a dust grain just above the disc photosphere: radiation pressure acts radially outward, gravity acts radially inward, and the grain's centrifugal force alone cannot lift its trajectory above a flared disc surface. Escape therefore requires vertical drag from the photoevaporative wind, which the simulations prescribe through a vertical gas velocity $v_{g,Z}=\dot{\Sigma}_{\rm wind}/\rho_g$. The code tracks a dust size distribution from $0.1\,\mu$m to $50$ cm, computes the radiation force per grain size via wavelength-dependent opacities and a 2D optical depth to the star, and removes any dust that crosses the wind base, defined by a neutral hydrogen column of $10^{21}\,\mathrm{cm}^{-2}$. The crucial diagnostic is the angle of the grain trajectory relative to the photosphere; micron-sized grains have trajectories that point back into the disc interior, so the outflow is geometrically unable to carry them away. A related mechanism is the pile-up of 'levitating' micron-sized grains at heights where wind drag balances settling, which sets the photosphere height and controls how much dust is exposed to direct stellar radiation.

What would settle it

Run the same dust-growth and radiative-transfer calculation with a full 2D gas velocity solution for the photoevaporative wind; if micron-sized grains at the inner rim then cross the wind base at rates above roughly $10^{-6}\,M_\oplus$ yr$^{-1}$, the paper's central negative result is overturned. Alternatively, a survey finding non-accreting transition discs with X-ray winds whose mid-IR excess fades within a few $10^5$ yr would contradict the predicted clearing timescales.

Watch

Extended reading notes

Core claim

The paper's central claim is that radiation-pressure-driven dust outflows remove dust from photoevaporating transition discs too slowly, by factors of 5–10, to prevent the inner edge of the outer disc from remaining optically thick to mid-infrared radiation for longer than observed. The simulations show that sub-micron grains are accelerated along trajectories that leave the disc, but micron-sized grains—which carry much of the outflow mass—are pushed radially outward and then re-enter the disc because their trajectories lie below the photosphere; the radial mass flux consequently falls by at least an order of magnitude between the dust trap and twice its radius. The trap is replenished by inward radial drift and by the outward sweeping of dust as photoevaporation pushes the gas inner rim outward, so in the fiducial models the dust-trap mass increases over 1 Myr after gap opening. The exception is an EUV wind with a smooth mass-loss profile and an unusually high photon flux, which leads to low dust masses at gap opening and a low photosphere that lets larger grains escape; in those runs the near-to-mid-IR excess fades within about 0.25–0.8 Myr. The authors conclude that the relic disc problem is not solved by radiation pressure, and that solutions must instead come from reducing the dust mass at gap opening or from revising the photoevaporation models themselves.

Load-bearing premise

The load-bearing assumption is that the photoevaporative wind can be treated as a purely vertical gas flow with the vertical velocity set by mass conservation, which exaggerates the upward drag on dust at the inner rim; if the real wind launches dust inward instead, the dust mass-loss rates computed here are upper limits.

Editorial extensions

If this is right

  • In the X-ray O11 and P19 photoevaporation models, radiation pressure does not reduce the dust-trap mass; the trap mass typically increases over 1 Myr after gap opening, so the discs remain mid-IR bright for too long.
  • The only successful cases are EUV winds with smooth mass-loss profiles and unusually high photon fluxes, where dust disperses within about 0.25–0.8 Myr; these require gas mass-loss rates above about $5\times10^{-9}\,M_\odot$ yr$^{-1}$ and dust masses below about $1\,M_\oplus$ at gap opening.
  • Radiation pressure competes with wind entrainment: it pushes dust outward and reduces the mass flux crossing the wind base at the inner rim, so including radiation pressure can lower, not raise, the dust lost to the wind.
  • The photosphere in photoevaporating discs is shaped by outflow grains rather than by shadowing from a hot inner rim, so the disc appears flared in scattered light even when the gas scale height is lower.
  • If current X-ray wind models overestimate gas mass-loss rates, as suggested by more recent hydrodynamic models, the computed dust mass-loss rates are upper limits and the negative conclusion becomes stronger.

Reading between the lines

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

  • Because dust mass-loss scales sub-linearly with dust surface density, discs that have already lost mass to planetesimal formation should show faster mid-IR fading after gap opening; this is testable with surveys that compare transition-disc lifetimes to initial dust masses.
  • The result that photosphere height is set by levitating outflow grains rather than shadowing implies that scattered-light scale-height measurements may overestimate vertical mixing; comparing scattered-light scale heights with gas scale heights from CO observations in photoevaporating discs would test this.
  • The vertical-drag prescription is likely generous to dust escape, so a full 2D gas velocity solution that includes the inward radial component of the wind at the inner rim would probably strengthen the negative conclusion rather than reverse it.
  • For discs evolving under MHD winds or external photoevaporation, where the gas outer radius shrinks and inward dust flux increases, radiation-pressure clearing should be even less efficient than in the purely viscous discs modelled here.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 6 minor

Summary. The paper investigates whether radiation-pressure-driven dust outflows can resolve the 'relic disc' problem in photoevaporating protoplanetary discs, in which models predict a population of non-accreting, large-cavity discs that is rarely observed. Using the cuDisc code, the authors couple 2D (R,Z) dust dynamics, coagulation/fragmentation, radiative transfer, and parameterised internal photoevaporation, evolving discs through the primordial phase in 1D and then through outer-disc dispersal in 2D. They measure dust mass-loss rates from the inner dust trap and run evolutionary simulations over ~1 Myr for three wind models (X-ray O11, X-ray P19, EUV), two stellar masses, and several fragmentation velocities and ionising fluxes. The central finding is that, in most of parameter space, radiation-pressure-driven outflows remove dust at rates roughly 5-10 times too small to deplete the dust trap against refilling, so radiation pressure does not solve the relic disc problem within current photoevaporation models; only smooth, EUV-like wind profiles with atypically high ionising fluxes and low dust masses at gap opening clear the trap on the required timescale. The paper also finds that the photosphere height is controlled by levitating micron-sized grains in the outflow rather than by inner-rim shadowing, and it presents synthetic SEDs and scattered-light images.

Significance. If the result holds, it closes a proposed solution to the relic disc problem and redirects attention to other dispersal mechanisms or to processes that reduce the dust mass at gap opening. The study is significant for its scope: it is, to my knowledge, the first global 2D treatment of radiation-pressure dust outflows in photoevaporating discs that includes coagulation/fragmentation and radiative transfer, with a parameter study spanning three wind models and a range of stellar and dust parameters. The public availability of cuDisc, the explicit discussion of approximation caveats, and the synthetic observations tied to a real non-accreting transition disc are concrete strengths. Importantly, the main simplifications (purely vertical wind, removal at the wind base, and use of extinction opacity for radiation pressure) all tend to overestimate dust removal, so the central negative result is conservative rather than fragile.

minor comments (6)
  1. [§3.2.1, Eq. (5)] The purely vertical wind prescription and the use of hydrostatic gas density in the wind region may overestimate vertical drag on dust near the inner rim, and the neglected radially inward launch of the wind would also reduce outward dust transport; because both effects bias the calculation in favour of dust removal, the central negative result is conservative. I recommend stating this one-sidedness explicitly in §8 and in the abstract rather than only in the §4 caveat.
  2. [§3.2.3, Eq. (6)] The radiation-pressure force per unit volume uses the extinction opacity κ_ext; for dust with anisotropic scattering the momentum-transfer efficiency should be κ_abs + (1-g)κ_sca. Using κ_ext overestimates the force, again in the conservative direction for the main conclusion, but the manuscript should either use the proper combination or add a sentence explaining why the difference is unimportant.
  3. [Table 1] The stellar radii are listed as '1.7 R_*' and '1.1 R_*'; these should be solar radii (R_sun) to avoid ambiguity, and the units in the table should be made consistent.
  4. [§3.2] Please clarify whether the 2D gas density, assumed hydrostatic, is recomputed as the dust distribution and temperature evolve during the 2D phase; if it is fixed at the initial condition, state this and comment on the expected effect on the vertical drag in Eq. (5).
  5. [§5.2.3] For the successful low-flux EUV case (Φ=10^43 s−1) the disc age at gap opening is 12 Myr, at the high end of observed disc lifetimes; this should be flagged more prominently when presenting this case as satisfying the observational constraints.
  6. [§3.2] There is a typo in the description of the solver: 'Godonuv' should be 'Godunov'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: negative result is a simulation output compared with, not fitted to, observed constraints.

full rationale

The paper's central claim is a negative result: radiation-pressure-driven dust outflows, within current photoevaporation models, cannot deplete the dust trap on the required timescales. The dust mass-loss rates quoted in Sections 4 and 5 are outputs of the cuDisc simulations, not parameters fitted to the relic-disc observations. The photoevaporation wind profiles (X-ray O11, X-ray P19, EUV) are external inputs with fixed strengths (L_X or Phi); the EUV flux is admittedly atypically large and is chosen to match X-ray gas mass-loss rates, but the paper does not present the EUV success as a validated prediction—it explicitly calls the conclusion unsatisfying. The required mass-loss rate of about 1e-6 M_earth/yr is derived from the observational constraint that dispersal must occur within roughly 1e5 years and typical trap masses, and is then compared with, not fitted to, the simulated rates. The vertical wind assumption v_g,Z = Sigma_wind/rho_g (Eq. 5) is a stated approximation with acknowledged caveats; if anything, overestimating vertical drag at the very inner rim would bias the simulation toward more dust removal, which would strengthen rather than create the negative conclusion. Self-citations to Owen et al. (2011), Picogna et al. (2019), and Robinson et al. (2024) are references to wind models and code infrastructure that are independently published and are not used to define the target result. No equation is defined in terms of the conclusion, no fitted parameter is renamed as a prediction, and the comparison against observations is external. Therefore no significant circularity is present.

Assumptions & free parameters 5 free parameters · 5 assumptions · 1 invented entities

The central negative result does not depend on a single fitted parameter but on the approximate treatment of the wind as a vertical flow and on the choice of photoevaporation models. The EUV success case requires an atypically large EUV flux, which is a significant assumption. The free parameters are mostly standard disc parameters, varied across a grid rather than fitted to the target observations.

free parameters (5)
  • EUV ionising flux Phi = 1e43 and 5e43 photons per second
    The high EUV flux is chosen to give similar gas mass-loss rates to the X-ray models, not calibrated to observed EUV fluxes. The EUV success case depends on this value.
  • Turbulence parameter alpha = 2.5e-3
    Chosen to match previous works and observed disc lifetimes; affects the maximum grain size and dust trap structure.
  • Dust fragmentation velocity v_frag = 5, 10, and 20 m/s
    Varied as part of the parameter study; determines the maximum grain size and thus the small-grain reservoir.
  • Dust-to-gas ratio floor = 1e-12
    Numerical floor to avoid division by small numbers; affects dust diffusion in low-density regions.
  • Wind base column density = 1e21 cm^-2
    Set to the X-ray penetration column; the authors argue the choice does not affect results because the wind base is far above the photosphere in the EUV runs.
assumptions (5)
  • domain assumption The photoevaporative wind can be approximated as a purely vertical gas flow with velocity v_{g,Z} = dot-Sigma_wind / rho_g (Section 3.2.1).
    The vertical velocity in the wind region is derived from mass conservation assuming hydrostatic gas density. The authors concede that at the inner rim, the wind is launched radially inwards before redirecting vertically, which is not captured.
  • domain assumption Dust that crosses the wind base is lost from the system (Section 3.2.4).
    The simulations stop at the wind base and floor any dust that crosses it, assuming it is certain to leave. If grains re-enter the disc, the mass-loss rates would be even lower, strengthening the paper's conclusion.
  • domain assumption The gas density in the wind region is hydrostatic (Section 3.2.1).
    This overestimates the gas density in the upper layers, but the authors argue the drag force depends on the mass flux, which is fixed by the wind mass-loss rate.
  • domain assumption The disc is axisymmetric and the gas is evolved in 1D (Section 3.2).
    cuDisc does not evolve the gas in 2D for computational reasons, so azimuthal and 2D gas structures are not captured.
  • domain assumption Dust growth and fragmentation are described by the Smoluchowski equation with a fixed grid of grain sizes (Section 3.2).
    The coagulation/fragmentation model is a standard approach in the field, but the fragmentation parameters, such as the fragment size distribution exponent, are assumed.
invented entities (1)
  • Levitating grains independent evidence
    purpose: Explains the height of the photosphere in photoevaporating discs.
    The levitating grain population is a model prediction that can be tested with scattered light observations: the photosphere height should be higher than the gas scale height. The paper shows synthetic scattered light images demonstrating this effect, and the mechanism can be tested by future observations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of The effect of radiation pressure on the dispersal of photoevaporating discs." pith.science (2026). https://pith.science/paper/YVOJZLO3

@misc{pith2026241205054,
  author       = {Pith},
  title        = {Pith review of: The effect of radiation pressure on the dispersal of photoevaporating discs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YVOJZLO3}},
  note         = {Machine review of arXiv:2412.05054}
}
abstract

Observed IR excesses indicate that protoplanetary discs evolve slowly for the majority of their lifetime before losing their near- and mid-IR excesses on short timescales. Photoevaporation models can explain this "two-timescale" nature of disc evolution through the removal of inner regions of discs after a few million years. However, they also predict the existence of a population of non-accreting discs with large cavities. Such discs are scarce within the observed population, suggesting the models are incomplete. We explore whether radiation-pressure-driven outflows are able to remove enough dust to fit observations. We simulate these outflows using cuDisc, including dust dynamics, growth/fragmentation, radiative transfer and a parameterisation of internal photoevaporation. We find that, in most cases, dust mass-loss rates are around 5-10 times too small to meet observational constraints. Particles are launched from the disc inner rim, however grains larger than around a micron do not escape in the outflow, meaning mass-loss rates are too low for the initial dust masses at gap-opening. Only systems that have smooth photoevaporation profiles with gas mass-loss rates $>\sim 5 \times 10^{-9}$ $M_\odot$ yr$^{-1}$ and disc dust masses $<\sim$1 $M_\oplus$ at the time of gap opening can meet observational constraints; in the current models these manifest as EUV winds driven by atypically large high-energy photon fluxes. We also find that the height of the disc's photosphere is controlled by small grains in the outflow as opposed to shadowing from a hot inner rim; the effect of this can be seen in synthetic scattered light observations.

Figures

Figures reproduced from arXiv: 2412.05054 by the authors.

Figure 1
Figure 1. A cartoon depicting the scenario in which dust can be removed from the disc in a radiation-pressure-driven outflow. Small dust grains suspended above the disc photosphere are impinged upon directly by stellar radiation, accelerating them into an outflow. These small grains at the surface must be replenished by fragmentation of large dust grains at the disc mid-plane. 10 1 10 0 10 1 10 2 10 3 10 4 Grain size [ m] 10 … view at source ↗
Figure 2
Figure 2. The 𝛽 parameter for different grain sizes and the two stellar types used in our suite of simulations. The effective temperatures and stellar radii that are appropriate for young stars of the shown mass can be seen in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. The forces acting on a dust grain suspended above the photosphere of the disc. Due to the cylindrically-radial centrifugal force on the grain, vertical drag from the photoevaporative wind is required in order for the resultant force on the grain to point at an angle above the mid-plane that is greater than the angle made between the mid-plane and the spherically-radial unit vector, 𝒓ˆ. This is important as the disc … view at source ↗
Figures from the paper (14 more)
Figure 4
Figure 4. Figure 4: A 1D simulation of disc evolution from the time of gap-opening until inner dust disc drainage. For this run, the gap opened after 3.6 Myr, and the inner dust disc had fully drained after 48,000 years. The opacity of the lines increases with time, with snapshots at 0, 1…
Figure 5
Figure 5. Figure 5: Surface density loss profiles for the different photoevaporative models listed in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: A snapshot of the fiducial X-ray O11 model after 10,000 years. The 2D densities and velocities of 3 different grain sizes are shown in the first column. To find the photosphere, the optical depth is calculated at a wavelength of 0.64 𝜇m, the location of the peak of the…
Figure 7
Figure 7. Figure 7: Aspect ratios of the photospheres, 𝐻phot/𝑅, for each fiducial wind model simulation. Dashed lines show the aspect ratios at the start of the simulations, before the outflow has formed, whilst the solid lines are after 4000 years of evolution. each parameter. We see tha…
Figure 8
Figure 8. Figure 8: The dependence of the radial mass flux of dust above the dust-trap on different simulation parameters, namely the total dust surface density, the flux of ionising radiation that controls photoevaporation, the turbulent 𝛼 and the fragmentation velocity. The results for …
Figure 9
Figure 9. Figure 9: The evolution of dust and gas surface density profiles for the fiducial X-ray O11 configuration with just photoevaporative (PE) effects (top panel) and with both PE and radiation pressure (RP) effects (bottom panel). Two different grain sizes are shown, representing sm…
Figure 10
Figure 10. Figure 10: 2D density and velocity profiles for two different grain sizes in the fiducial X-ray O11 model. The left and right columns show simulations with only photoevaporative (PE) effects and with both PE and radiation pressure (RP) effects respectively. The top and bottom ro…
Figure 12
Figure 12. Figure 12: The total mass-loss rate of dust through the wind base for the fiducial X-ray O11 simulation, for both the model with just photoevaporative (PE) effects and the model with PE and radiation pressure (RP) effects. This snapshot is after 75,000 years of evolution. 5.2.1 …
Figure 13
Figure 13. Figure 13: The average mass-loss rates and final dust-trap masses for the X-ray O11 parameter study with the 0.7 𝑀⊙star. The colour-map indicates the mass-loss rates whilst the numbers in each box indicate the final dust masses, 1 Myr after gap-opening. 5.2.2 X-ray P19 model As …
Figure 15
Figure 15. Figure 15: The vertically-integrated grain-size distribution with respect to radius for each of the three wind models. The parameters for each of the models are; X-ray O11: log10 𝐿𝑋 = 30, 𝑣frag = 10 m s−1 , X-ray P19: log10 𝐿𝑋 = 30.3, 𝑣frag = 5 m s−1 , EUV: Φ = 5 × 1043 photons …
Figure 17
Figure 17. Figure 17: The dust grain-size distribution with respect to height (grey con￾tours) after 105 years at a radius of 13 au, behind the dust-trap, for the fiducial X-ray O11 simulation. The red/blue, filled contours show the overall produc￾tion/destruction rates of grains due to co…
Figure 16
Figure 16. Figure 16: The outflow of micron-sized grains formed for each of the simu￾lations shown in fig. 15. All models are shown at a snapshot time of 100,000 years. that the longevity of the mid-to-far IR flux is incompatible with the population level statistics of disc observations. A…
Figure 18
Figure 18. Figure 18: Spectral energy distributions for simulations from each of the different winds models. The line opacity increases with time. The snapshot times after gap-opening for each of these models are; X-ray O11: 0, 0.5 & 1 Myr, X-ray P19: 0, 0.125 & 0.25 Myr and EUV: 0, 0.15, …
Figure 19
Figure 19. Figure 19: Scattered light images of discs from the three wind models. These false colour images use the intensity of light at 0.8, 2, and 8 𝜇m for the blue, green, and red channels respectively. These particular snapshots are after 100,000 years of evolution. the X-ray models s…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

85 extracted references · 7 canonical work pages

  1. [1]

    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.state := if if FUNCTION not #0 #1 if FUNCTION and 'skip pop #0 if FUNCTION or pop #1...

  2. [4]

    D., Clarke C

    Alexander R. D., Clarke C. J., Pringle J. E., 2006b, @doi [ ] 10.1111/j.1365-2966.2006.10294.x , https://ui.adsabs.harvard.edu/abs/2006MNRAS.369..229A 369, 229

    arXiv 2006

  3. [5]

    J., Simon J

    Armitage P. J., Simon J. B., Martin R. G., 2013, @doi [ ] 10.1088/2041-8205/778/1/L14 , https://ui.adsabs.harvard.edu/abs/2013ApJ...778L..14A 778, L14

    doi:10.1088/2041-8205/778/1/l14 2013

  4. [6]

    H., 1996, @doi [ ] 10.1086/310200 , https://ui.adsabs.harvard.edu/abs/1996ApJ...467L..77A 467, L77

    Artymowicz P., Lubow S. H., 1996, @doi [ ] 10.1086/310200 , https://ui.adsabs.harvard.edu/abs/1996ApJ...467L..77A 467, L77

    doi:10.1086/310200 1996

  5. [7]

    Bai X.-N., 2016, @doi [ ] 10.3847/0004-637X/821/2/80 , https://ui.adsabs.harvard.edu/abs/2016ApJ...821...80B 821, 80

    doi:10.3847/0004-637x/821/2/80 2016

  6. [8]

    M., 2013, @doi [ ] 10.1088/0004-637X/769/1/76 , https://ui.adsabs.harvard.edu/abs/2013ApJ...769...76B 769, 76

    Bai X.-N., Stone J. M., 2013, @doi [ ] 10.1088/0004-637X/769/1/76 , https://ui.adsabs.harvard.edu/abs/2013ApJ...769...76B 769, 76

    doi:10.1088/0004-637x/769/1/76 2013

  7. [9]

    A., Hawley J

    Balbus S. A., Hawley J. F., 1991, @doi [ ] 10.1086/170270 , https://ui.adsabs.harvard.edu/abs/1991ApJ...376..214B 376, 214

    doi:10.1086/170270 1991

  8. [10]

    Birnstiel T., 2018, birnstiel/dsharp\_opac: revised release of package, @doi 10.5281/zenodo.1495277 , https://doi.org/10.5281/zenodo.1495277

    doi:10.5281/zenodo.1495277 2018

Show all 85 references
  1. [11]

    P., Brauer F., 2009, @doi [ ] 10.1051/0004-6361/200912452 , https://ui.adsabs.harvard.edu/abs/2009A&A...503L...5B 503, L5

    Birnstiel T., Dullemond C. P., Brauer F., 2009, @doi [ ] 10.1051/0004-6361/200912452 , https://ui.adsabs.harvard.edu/abs/2009A&A...503L...5B 503, L5

    2009 doi

  2. [12]

    P., Brauer F., 2010, @doi [ ] 10.1051/0004-6361/200913731 , https://ui.adsabs.harvard.edu/abs/2010A&A...513A..79B 513, A79

    Birnstiel T., Dullemond C. P., Brauer F., 2010, @doi [ ] 10.1051/0004-6361/200913731 , https://ui.adsabs.harvard.edu/abs/2010A&A...513A..79B 513, A79

    2010 doi

  3. [13]

    W., Dullemond C

    Birnstiel T., Ormel C. W., Dullemond C. P., 2011, @doi [ ] 10.1051/0004-6361/201015228 , https://ui.adsabs.harvard.edu/abs/2011A&A...525A..11B 525, A11

    2011 doi

  4. [14]

    Birnstiel T., Klahr H., Ercolano B., 2012, @doi [ ] 10.1051/0004-6361/201118136 , https://ui.adsabs.harvard.edu/abs/2012A&A...539A.148B 539, A148

    2012 doi

  5. [15]

    Birnstiel T., et al., 2018, @doi [ ] 10.3847/2041-8213/aaf743 , 869, L45

    2018 doi

  6. [16]

    D., Payne D

    Blandford R. D., Payne D. G., 1982, @doi [ ] 10.1093/mnras/199.4.883 , https://ui.adsabs.harvard.edu/abs/1982MNRAS.199..883B 199, 883

    1982 doi

  7. [17]

    A., Clarke C

    Booth R. A., Clarke C. J., 2021, @doi [ ] 10.1093/mnras/stab090 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.1569B 502, 1569

    2021 doi

  8. [18]

    I., Goldreich P., 1997, @doi [ ] 10.1086/304869 , https://ui.adsabs.harvard.edu/abs/1997ApJ...490..368C 490, 368

    Chiang E. I., Goldreich P., 1997, @doi [ ] 10.1086/304869 , https://ui.adsabs.harvard.edu/abs/1997ApJ...490..368C 490, 368

    1997 doi

  9. [19]

    D., 2016, @doi [ ] 10.3847/0004-637X/823/2/102 , https://ui.adsabs.harvard.edu/abs/2016ApJ...823..102C 823, 102

    Choi J., Dotter A., Conroy C., Cantiello M., Paxton B., Johnson B. D., 2016, @doi [ ] 10.3847/0004-637X/823/2/102 , https://ui.adsabs.harvard.edu/abs/2016ApJ...823..102C 823, 102

    2016 doi

  10. [20]

    A., et al., 2010, @doi [ ] 10.1088/0004-637X/712/2/925 , https://ui.adsabs.harvard.edu/abs/2010ApJ...712..925C 712, 925

    Cieza L. A., et al., 2010, @doi [ ] 10.1088/0004-637X/712/2/925 , https://ui.adsabs.harvard.edu/abs/2010ApJ...712..925C 712, 925

    2010 doi

  11. [21]

    J., Gendrin A., Sotomayor M., 2001, @doi [ ] 10.1046/j.1365-8711.2001.04891.x , https://ui.adsabs.harvard.edu/abs/2001MNRAS.328..485C 328, 485

    Clarke C. J., Gendrin A., Sotomayor M., 2001, @doi [ ] 10.1046/j.1365-8711.2001.04891.x , https://ui.adsabs.harvard.edu/abs/2001MNRAS.328..485C 328, 485

    2001

  12. [22]

    Coleman G. A. L., Mroueh J. K., Haworth T. J., 2024, @doi [ ] 10.1093/mnras/stad3692 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.527.7588C 527, 7588

    2024 doi

  13. [23]

    S., 1969, @doi [ ] 10.1029/JB074i010p02531 , https://ui.adsabs.harvard.edu/abs/1969JGR....74.2531D 74, 2531

    Dohnanyi J. S., 1969, @doi [ ] 10.1029/JB074i010p02531 , https://ui.adsabs.harvard.edu/abs/1969JGR....74.2531D 74, 2531

    1969 doi

  14. [24]

    T., 2003, @doi [ ] 10.1086/379123 , https://ui.adsabs.harvard.edu/abs/2003ApJ...598.1026D 598, 1026

    Draine B. T., 2003, @doi [ ] 10.1086/379123 , https://ui.adsabs.harvard.edu/abs/2003ApJ...598.1026D 598, 1026

    2003 doi

  15. [25]

    Dubrulle B., Morfill G., Sterzik M., 1995, @doi [ ] 10.1006/icar.1995.1058 , https://ui.adsabs.harvard.edu/abs/1995Icar..114..237D 114, 237

    1995

  16. [26]

    P., Dominik C., Natta A., 2001, @doi [ ] 10.1086/323057 , https://ui.adsabs.harvard.edu/abs/2001ApJ...560..957D 560, 957

    Dullemond C. P., Dominik C., Natta A., 2001, @doi [ ] 10.1086/323057 , https://ui.adsabs.harvard.edu/abs/2001ApJ...560..957D 560, 957

    2001 doi

  17. [27]

    Dullemond C. P., Juhasz A., Pohl A., Sereshti F., Shetty R., Peters T., Commercon B., Flock M., 2012, RADMC-3D: A multi-purpose radiative transfer tool , Astrophysics Source Code Library, record ascl:1202.015

    2012

  18. [28]

    E., 2016, @doi [ ] 10.1093/mnras/stw1179 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.460.3472E 460, 3472

    Ercolano B., Owen J. E., 2016, @doi [ ] 10.1093/mnras/stw1179 , https://ui.adsabs.harvard.edu/abs/2016MNRAS.460.3472E 460, 3472

    2016 doi

  19. [29]

    Ercolano B., Pascucci I., 2017, @doi [Royal Society Open Science] 10.1098/rsos.170114 , https://ui.adsabs.harvard.edu/abs/2017RSOS....470114E 4, 170114

    2017 doi

  20. [30]

    J., Drake J

    Ercolano B., Clarke C. J., Drake J. J., 2009, @doi [ ] 10.1088/0004-637X/699/2/1639 , https://ui.adsabs.harvard.edu/abs/2009ApJ...699.1639E 699, 1639

    2009 doi

  21. [31]

    Ercolano B., Picogna G., Monsch K., 2023, @doi [ ] 10.1093/mnrasl/slad123 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.526L.105E 526, L105

    2023 doi

  22. [32]

    Espaillat C., Andrews S., Powell D., Feldman D., Qi C., Wilner D., D'Alessio P., 2015, @doi [ ] 10.1088/0004-637X/807/2/156 , https://ui.adsabs.harvard.edu/abs/2015ApJ...807..156E 807, 156

    2015 doi

  23. [33]

    S., McCarthy I

    Font A. S., McCarthy I. G., Johnstone D., Ballantyne D. R., 2004, @doi [ ] 10.1086/383518 , https://ui.adsabs.harvard.edu/abs/2004ApJ...607..890F 607, 890

    2004 doi

  24. [34]

    Franz R., Picogna G., Ercolano B., Casassus S., Birnstiel T., Rab C., P \'e rez S., 2022, @doi [ ] 10.1051/0004-6361/202142785 , https://ui.adsabs.harvard.edu/abs/2022A&A...659A..90F 659, A90

    2022 doi

  25. [35]

    F., 1996, @doi [ ] 10.1086/176735 , https://ui.adsabs.harvard.edu/abs/1996ApJ...457..355G 457, 355

    Gammie C. F., 1996, @doi [ ] 10.1086/176735 , https://ui.adsabs.harvard.edu/abs/1996ApJ...457..355G 457, 355

    1996 doi

  26. [36]

    J., 2019, @doi [ ] 10.3847/1538-4357/ab311a , https://ui.adsabs.harvard.edu/abs/2019ApJ...882...33G 882, 33

    Giacalone S., Teitler S., K \"o nigl A., Krijt S., Ciesla F. J., 2019, @doi [ ] 10.3847/1538-4357/ab311a , https://ui.adsabs.harvard.edu/abs/2019ApJ...882...33G 882, 33

    2019 doi

  27. [37]

    Gorti U., Hollenbach D., 2009, @doi [ ] 10.1088/0004-637X/690/2/1539 , https://ui.adsabs.harvard.edu/abs/2009ApJ...690.1539G 690, 1539

    2009 doi

  28. [38]

    Hardy A., et al., 2015, , 583, A66

    2015

  29. [39]

    Hartmann L., Calvet N., Gullbring E., D'Alessio P., 1998, @doi [ ] 10.1086/305277 , https://ui.adsabs.harvard.edu/abs/1998ApJ...495..385H 495, 385

    1998 doi

  30. [40]

    J., Clarke C

    Haworth T. J., Clarke C. J., Owen J. E., 2016, , 457, 1905

    2016

  31. [41]

    Henning T., Stognienko R., 1996, , https://ui.adsabs.harvard.edu/abs/1996A&A...311..291H 311, 291

    1996

  32. [42]

    Hollenbach D., Johnstone D., Lizano S., Shu F., 1994, @doi [ ] 10.1086/174276 , https://ui.adsabs.harvard.edu/abs/1994ApJ...428..654H 428, 654

    1994 doi

  33. [43]

    A., Clarke C

    Hutchison M. A., Clarke C. J., 2021, @doi [ ] 10.1093/mnras/staa3608 , https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.1127H 501, 1127

    2021 doi

  34. [44]

    Komaki A., Nakatani R., Yoshida N., 2021, @doi [ ] 10.3847/1538-4357/abe2af , https://ui.adsabs.harvard.edu/abs/2021ApJ...910...51K 910, 51

    2021 doi

  35. [45]

    E., 1974, @doi [ ] 10.1093/mnras/168.3.603 , https://ui.adsabs.harvard.edu/abs/1974MNRAS.168..603L 168, 603

    Lynden-Bell D., Pringle J. E., 1974, @doi [ ] 10.1093/mnras/168.3.603 , https://ui.adsabs.harvard.edu/abs/1974MNRAS.168..603L 168, 603

    1974 doi

  36. [46]

    F., Ansdell M., Rosotti G

    Manara C. F., Ansdell M., Rosotti G. P., Hughes A. M., Armitage P. J., Lodato G., Williams J. P., 2023, in Inutsuka S., Aikawa Y., Muto T., Tomida K., Tamura M., eds, Astronomical Society of the Pacific Conference Series Vol. 534, Protostars and Planets VII. p. 539 ( @eprint a...

    2023 doi arXiv

  37. [47]

    S., Rumpl W., Nordsieck K

    Mathis J. S., Rumpl W., Nordsieck K. H., 1977, @doi [ ] 10.1086/155591 , https://ui.adsabs.harvard.edu/abs/1977ApJ...217..425M 217, 425

    1977 doi

  38. [48]

    Nakatani R., Hosokawa T., Yoshida N., Nomura H., Kuiper R., 2018, @doi [ ] 10.3847/1538-4357/aad9fd , https://ui.adsabs.harvard.edu/abs/2018ApJ...865...75N 865, 75

    2018 doi

  39. [49]

    Ohtsuki K., Nakagawa Y., Nakazawa K., 1990, @doi [ ] 10.1016/0019-1035(90)90015-2 , https://ui.adsabs.harvard.edu/abs/1990Icar...83..205O 83, 205

    1990 doi

  40. [50]

    E., Clarke C

    Owen J. E., Clarke C. J., 2012, @doi [ ] 10.1111/j.1745-3933.2012.01334.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.426L..96O 426, L96

    2012

  41. [51]

    E., Kollmeier J

    Owen J. E., Kollmeier J. A., 2019, @doi [ ] 10.1093/mnras/stz1591 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.487.3702O 487, 3702

    2019 doi

  42. [52]

    E., Ercolano B., Clarke C

    Owen J. E., Ercolano B., Clarke C. J., Alexander R. D., 2010, @doi [ ] 10.1111/j.1365-2966.2009.15771.x , https://ui.adsabs.harvard.edu/abs/2010MNRAS.401.1415O 401, 1415

    2010

  43. [54]

    E., Ercolano B., Clarke C

    Owen J. E., Ercolano B., Clarke C. J., 2011b, @doi [ ] 10.1111/j.1365-2966.2010.17818.x , https://ui.adsabs.harvard.edu/abs/2011MNRAS.412...13O 412, 13

    2010

  44. [55]

    E., Clarke C

    Owen J. E., Clarke C. J., Ercolano B., 2012, , 422, 1880

    2012

  45. [56]

    E., Hudoba de Badyn M., Clarke C

    Owen J. E., Hudoba de Badyn M., Clarke C. J., Robins L., 2013, , 436, 1430

    2013

  46. [57]

    P., Brooks K

    Pascucci I., Ricci L., Gorti U., Hollenbach D., Hendler N. P., Brooks K. J., Contreras Y., 2014, @doi [ ] 10.1088/0004-637X/795/1/1 , https://ui.adsabs.harvard.edu/abs/2014ApJ...795....1P 795, 1

    2014 doi

  47. [58]

    Perez-Becker D., Chiang E., 2011, @doi [ ] 10.1088/0004-637X/727/1/2 , https://ui.adsabs.harvard.edu/abs/2011ApJ...727....2P 727, 2

    2011 doi

  48. [59]

    E., Weber M

    Picogna G., Ercolano B., Owen J. E., Weber M. L., 2019, @doi [ ] 10.1093/mnras/stz1166 , https://ui.adsabs.harvard.edu/abs/2019MNRAS.487..691P 487, 691

    2019 doi

  49. [60]

    E., 1981, @doi [ ] 10.1146/annurev.aa.19.090181.001033 , https://ui.adsabs.harvard.edu/abs/1981ARA&A..19..137P 19, 137

    Pringle J. E., 1981, @doi [ ] 10.1146/annurev.aa.19.090181.001033 , https://ui.adsabs.harvard.edu/abs/1981ARA&A..19..137P 19, 137

    1981

  50. [61]

    E., Norman C

    Pudritz R. E., Norman C. A., 1983, @doi [ ] 10.1086/161481 , https://ui.adsabs.harvard.edu/abs/1983ApJ...274..677P 274, 677

    1983 doi

  51. [62]

    Rab C., et al., 2022, @doi [ ] 10.1051/0004-6361/202244362 , https://ui.adsabs.harvard.edu/abs/2022A&A...668A.154R 668, A154

    2022 doi

  52. [63]

    P., 2012, @doi [ ] 10.1111/j.1365-2966.2011.19834.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.419.1701R 419, 1701

    Reg \'a ly Z., Juh \'a sz A., S \'a ndor Z., Dullemond C. P., 2012, @doi [ ] 10.1111/j.1365-2966.2011.19834.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.419.1701R 419, 1701

    2012

  53. [64]

    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

  54. [65]

    W., 2000, @doi [ ] 10.1086/309198 , https://ui.adsabs.harvard.edu/abs/2000ApJ...539..258R 539, 258

    Richling S., Yorke H. W., 2000, @doi [ ] 10.1086/309198 , https://ui.adsabs.harvard.edu/abs/2000ApJ...539..258R 539, 258

    2000 doi

  55. [66]

    A., Owen J

    Robinson A., Booth R. A., Owen J. E., 2024, @doi [ ] 10.1093/mnras/stae624 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.529.1524R 529, 1524

    2024 doi

  56. [67]

    D., Booth R

    Sellek A. D., Booth R. A., Clarke C. J., 2020, @doi [ ] 10.1093/mnras/stz3528 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.492.1279S 492, 1279

    2020 doi

  57. [68]

    D., Grassi T., Picogna G., Rab C., Clarke C

    Sellek A. D., Grassi T., Picogna G., Rab C., Clarke C. J., Ercolano B., 2024, @doi [ ] 10.1051/0004-6361/202450171 , https://ui.adsabs.harvard.edu/abs/2024A&A...690A.296S 690, A296

    2024 doi

  58. [69]

    I., Sunyaev R

    Shakura N. I., Sunyaev R. A., 1973, , 24, 337

    1973

  59. [70]

    H., Shang H., Lee T., 1996, @doi [Science] 10.1126/science.271.5255.1545 , https://ui.adsabs.harvard.edu/abs/1996Sci...271.1545S 271, 1545

    Shu F. H., Shang H., Lee T., 1996, @doi [Science] 10.1126/science.271.5255.1545 , https://ui.adsabs.harvard.edu/abs/1996Sci...271.1545S 271, 1545

    1996

  60. [71]

    F., Tazzari M., 2023, @doi [ ] 10.3847/2041-8213/acf048 , https://ui.adsabs.harvard.edu/abs/2023ApJ...954L..13S 954, L13

    Somigliana A., Testi L., Rosotti G., Toci C., Lodato G., Tabone B., Manara C. F., Tazzari M., 2023, @doi [ ] 10.3847/2041-8213/acf048 , https://ui.adsabs.harvard.edu/abs/2023ApJ...954L..13S 954, L13

    2023 doi

  61. [72]

    M., Gardiner T., 2009, @doi [New Astronomy] https://doi.org/10.1016/j.newast.2008.06.003 , 14, 139

    Stone J. M., Gardiner T., 2009, @doi [New Astronomy] https://doi.org/10.1016/j.newast.2008.06.003 , 14, 139

    2009 doi

  62. [73]

    M., Strom S

    Strom K. M., Strom S. E., Edwards S., Cabrit S., Skrutskie M. F., 1989, @doi [ ] 10.1086/115085 , https://ui.adsabs.harvard.edu/abs/1989AJ.....97.1451S 97, 1451

    1989 doi

  63. [74]

    R., Bessell M

    Sung H., Stauffer J. R., Bessell M. S., 2009, @doi [ ] 10.1088/0004-6256/138/4/1116 , https://ui.adsabs.harvard.edu/abs/2009AJ....138.1116S 138, 1116

    2009 doi

  64. [75]

    P., Cridland A

    Tabone B., Rosotti G. P., Cridland A. J., Armitage P. J., Lodato G., 2022, @doi [ ] 10.1093/mnras/stab3442 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.512.2290T 512, 2290

    2022 doi

  65. [76]

    Takeuchi T., Lin D. N. C., 2003, @doi [ ] 10.1086/376496 , https://ui.adsabs.harvard.edu/abs/2003ApJ...593..524T 593, 524

    2003 doi

  66. [77]

    Tanaka H., Inaba S., Nakazawa K., 1996, @doi [Icarus] https://doi.org/10.1006/icar.1996.0170 , 123, 450

    1996

  67. [78]

    Wang L., Goodman J., 2017, @doi [ ] 10.3847/1538-4357/aa8726 , https://ui.adsabs.harvard.edu/abs/2017ApJ...847...11W 847, 11

    2017 doi

  68. [79]

    G., Brandt R

    Warren S. G., Brandt R. E., 2008, @doi [Journal of Geophysical Research (Atmospheres)] 10.1029/2007JD009744 , https://ui.adsabs.harvard.edu/abs/2008JGRD..11314220W 113, D14220

    2008 doi

  69. [80]

    L., Ercolano B., Picogna G., Hartmann L., Rodenkirch P

    Weber M. L., Ercolano B., Picogna G., Hartmann L., Rodenkirch P. J., 2020, @doi [ ] 10.1093/mnras/staa1549 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.496..223W 496, 223

    2020 doi

  70. [81]

    Weder J., Mordasini C., Emsenhuber A., 2023, @doi [ ] 10.1051/0004-6361/202243453 , https://ui.adsabs.harvard.edu/abs/2023A&A...674A.165W 674, A165

    2023 doi

  71. [82]

    J., Haworth T

    Winter A. J., Haworth T. J., 2022, @doi [European Physical Journal Plus] 10.1140/epjp/s13360-022-03314-1 , https://ui.adsabs.harvard.edu/abs/2022EPJP..137.1132W 137, 1132

    2022 doi

  72. [83]

    C., Pani \'c O., Kennedy G

    Wyatt M. C., Pani \'c O., Kennedy G. M., Matr \`a L., 2015, @doi [ ] 10.1007/s10509-015-2315-6 , https://ui.adsabs.harvard.edu/abs/2015Ap&SS.357..103W 357, 103

    2015 doi

  73. [84]

    G., Mennella V., Colangeli L., Bussoletti E., 1996, @doi [ ] 10.1093/mnras/282.4.1321 , https://ui.adsabs.harvard.edu/abs/1996MNRAS.282.1321Z 282, 1321

    Zubko V. G., Mennella V., Colangeli L., Bussoletti E., 1996, @doi [ ] 10.1093/mnras/282.4.1321 , https://ui.adsabs.harvard.edu/abs/1996MNRAS.282.1321Z 282, 1321

    1996 doi

  74. [85]

    van Boekel R., Min M., Waters L. B. F. M., de Koter A., Dominik C., van den Ancker M. E., Bouwman J., 2005, @doi [ ] 10.1051/0004-6361:20042339 , https://ui.adsabs.harvard.edu/abs/2005A&A...437..189V 437, 189

    2005 doi

  75. [86]

    van Leer B., 1974, @doi [Journal of Computational Physics] https://doi.org/10.1016/0021-9991(74)90019-9 , 14, 361

    1974 doi

  76. [87]

    W., van Terwisga S., Mer \' n B., Herczeg G., Ligterink N

    van der Marel N., Verhaar B. W., van Terwisga S., Mer \' n B., Herczeg G., Ligterink N. F. W., van Dishoeck E. F., 2016, @doi [ ] 10.1051/0004-6361/201628075 , https://ui.adsabs.harvard.edu/abs/2016A&A...592A.126V 592, A126

    2016 doi

  77. [88]

    van der Marel N., et al., 2018, @doi [ ] 10.3847/1538-4357/aaaa6b , https://ui.adsabs.harvard.edu/abs/2018ApJ...854..177V 854, 177

    2018 doi

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.