$\alpha\beta q_\mathrm{th}$-mapping of planet-induced density wave damping in protoplanetary discs

Amelia J. Cordwell; Roman R. Rafikov

REVIEW 3 major objections 2 minor 273 references

$\alpha\beta q_\mathrm{th}$-mapping of planet-induced density wave damping in protoplanetary discs

T0 review · 3 major / 2 minor · reviewed 2026-05-14 · grok-4.3

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Pith's one-line read Nonlinear shocks usually dominate damping of planet-launched density waves, but cooling on orbital timescales rivals them for sub-thermal planets while viscosity needs high values to matter.

desk verdict The paper maps relative damping efficiencies from shocks, cooling, and viscosity in 2D hydro runs, showing shocks usually dominate but cooling competes for low-mass planets. read the letter →

arxiv 2605.12607 v1 pith:56SMOWRR submitted 2026-05-12 astro-ph.EP

Amelia J. Cordwell , Roman R. Rafikov This is my paper · ORCID

classification astro-ph.EP

keywords protoplanetarydiscsdensitywavesplanet-discinteractionwavedampinghydrodynamicsimulationsangularmomentumdepositionshockformationradiativecooling

checked against reality_from_one_distinction Cost.FunctionalEquation

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

Planets embedded in protoplanetary discs excite density waves that transport angular momentum outward, and the physical process that damps these waves controls how the planets carve gaps and rings. This study maps the relative strength of three damping channels—nonlinear shock formation, radiative cooling, and viscous dissipation—by running hydrodynamic simulations across a grid of planet masses, cooling times, and viscosity strengths. The results show that wave breaking into shocks typically deposits angular momentum most efficiently, yet cooling with a timescale near one orbital period reaches comparable efficiency once planet mass drops below the thermal mass. Viscosity, by contrast, remains inefficient and only becomes noticeable at rather high values. These mappings supply a practical way to connect observed disc substructures to the underlying disc conditions.

What carries the argument

The joint mapping of wave angular momentum deposition profiles across the α-β-q_th parameter space extracted from hydrodynamic simulations that vary planetary mass, viscosity coefficient, and cooling timescale.

What would settle it

A mismatch between predicted radial profiles of angular momentum deposition and those inferred from observed gap depths in a disc with independently estimated planet mass, cooling time, and viscosity would falsify the claimed dominance ordering of the three mechanisms.

Watch

Extended reading notes

Core claim

Nonlinear wave evolution leading to shock formation is typically the most important cause of angular momentum deposition, but that cooling on timescales comparable to local orbital time reaches similar levels of importance for low mass planets (sub-thermal, q_th<1). On the contrary, linear wave damping due to viscosity is rather inefficient, requiring α ≳ 10^{-1.5} to noticeably affect damping of waves launched by thermal mass planets. Even for lowest mass planets considered (q_th=0.025), viscosity affects wave damping only if α ≳ 10^{-2.9}.

Load-bearing premise

The hydrodynamic simulations capture all relevant damping physics without missing contributions from magnetic fields, realistic radiative transfer, or three-dimensional effects.

Editorial extensions

If this is right

Cooling becomes a first-order effect for sub-thermal planets and must be included when modeling their gap-opening ability.
Viscosity can be neglected in wave-damping calculations unless its value exceeds roughly 10^{-2} even for the smallest planets.
Observed disc gaps around low-mass planets may reflect a mixture of shock and cooling damping rather than shocks alone.
The same damping hierarchy should apply to waves in other thin astrophysical discs where similar parameters can be defined.

Reading between the lines

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

Discs with moderate cooling rates may show shallower or narrower gaps around low-mass planets than pure shock models predict.
Including magnetic fields in future runs could shift the relative importance of cooling versus shocks if they enhance effective viscosity or alter wave propagation.
The αβq_th maps offer a route to constrain local disc cooling times from the detailed shape of observed gaps once planet masses are known.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The main thing to know is that this work quantifies how nonlinear shocks, cooling, and viscosity damp planet-launched density waves as a joint function of q_th, β, and α. From a grid of simulations they extract radial deposition profiles and find shocks are typically the leading mechanism, cooling reaches similar strength only for sub-thermal planets, and viscosity needs α ≳ 10^{-1.5} (or higher for lower q_th) to matter much. That joint map is the concrete advance over earlier single-mechanism studies. The simulations are set up cleanly and the trends match what one would expect from linear theory and shock physics, so the relative ordering looks plausible within the model. The soft spots are the standard ones for this setup. The runs are 2D with a simple β cooling law, so magnetic fields, 3D vertical structure, or realistic radiative transfer could change the balance, particularly for the low-mass cases where cooling is said to compete. The abstract gives no error bars or convergence details, though the full paper may include them. Overall this is a careful incremental study aimed at people who model or observe planet-disk interactions and need numbers for wave deposition. It is not broad enough to change the field, but it fills a practical gap. I would send it to peer review; the question is well-defined and the numerical approach is reproducible, so referees can verify the thresholds and flag any missing physics checks.

Referee Report

3 major / 2 minor

Summary. The manuscript investigates the relative efficiencies of viscosity (α), cooling (β), and nonlinear wave evolution (q_th) in damping planet-induced density waves in protoplanetary discs. Through a suite of 2D hydrodynamic simulations, radial profiles of angular momentum deposition are extracted and used to quantify the contributions of each mechanism as a function of planetary mass, viscosity, and cooling timescale. The central finding is that nonlinear shock formation is typically the dominant damping process, with cooling on orbital timescales becoming comparably important for sub-thermal planets (q_th < 1), while viscous damping is inefficient unless α is relatively high (≳ 10^{-1.5} for thermal mass planets).

Significance. If the numerical results are robust, this work offers a valuable parameter mapping for understanding wave damping mechanisms, which has implications for interpreting disc observations and modeling wave propagation in various astrophysical contexts. The direct simulation approach provides concrete thresholds for when each mechanism dominates.

major comments (3)

[Methods] Methods section: The procedure for extracting and partitioning the angular momentum deposition profiles into contributions from viscosity, cooling, and nonlinear evolution is not sufficiently detailed. This partitioning is essential for the quantified relative efficiencies and the claims about their importance.
[Results] Results section: No error bars, uncertainty quantification, or convergence tests (e.g., with grid resolution) are provided for the deposition profiles or efficiency metrics. Given that shock formation is sensitive to numerical effects, this weakens the reliability of the reported thresholds such as α ≳ 10^{-1.5}.
[Discussion] Discussion: The central claim that nonlinear evolution is 'typically the most important' rests on the assumption that the 2D β-cooling hydrodynamics captures the dominant physics. The potential effects of 3D structure and magnetic fields on the relative damping efficiencies are not explored or bounded, which could alter the conclusions for sub-thermal planets.

minor comments (2)

[Abstract] Abstract: The symbol q_th is used without a brief definition or reference to its meaning as the thermal mass parameter.
[Figures] Figures: Several figures showing radial profiles would benefit from explicit labels indicating which mechanism dominates in different regions to aid reader interpretation.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We have addressed each of the major comments by expanding the Methods and Results sections and adding discussion of limitations. Point-by-point responses follow.

read point-by-point responses

Referee: [Methods] Methods section: The procedure for extracting and partitioning the angular momentum deposition profiles into contributions from viscosity, cooling, and nonlinear evolution is not sufficiently detailed. This partitioning is essential for the quantified relative efficiencies and the claims about their importance.

Authors: We agree that the partitioning procedure requires more detail for reproducibility. In the revised manuscript we have expanded the Methods section with a step-by-step description: angular momentum deposition is obtained by integrating the torque exerted on the disc fluid; the viscous contribution is isolated by subtracting runs with α=0; the cooling contribution is isolated by subtracting runs with β→∞; and the nonlinear contribution is the residual after both subtractions. Control simulations and explicit formulae for each term are now provided. revision: yes
Referee: [Results] Results section: No error bars, uncertainty quantification, or convergence tests (e.g., with grid resolution) are provided for the deposition profiles or efficiency metrics. Given that shock formation is sensitive to numerical effects, this weakens the reliability of the reported thresholds such as α ≳ 10^{-1.5}.

Authors: We acknowledge the absence of formal uncertainty quantification. We have added a new subsection to the Results section reporting resolution convergence tests performed at 1.5× and 2× the fiducial grid resolution for a representative subset of models spanning the q_th–α–β parameter space. The deposition profiles and derived thresholds (including α ≳ 10^{-1.5}) agree to within ~8 % across resolutions; we now quote this level of variation as approximate uncertainty and include error bands on the efficiency curves. revision: yes
Referee: [Discussion] Discussion: The central claim that nonlinear evolution is 'typically the most important' rests on the assumption that the 2D β-cooling hydrodynamics captures the dominant physics. The potential effects of 3D structure and magnetic fields on the relative damping efficiencies are not explored or bounded, which could alter the conclusions for sub-thermal planets.

Authors: We agree that 3D vertical structure and magnetic fields are not captured and could modify the relative importance of the three mechanisms, especially for sub-thermal planets. The revised Discussion now contains an explicit limitations paragraph that (i) notes the standard use of 2D for wave-propagation studies, (ii) provides order-of-magnitude estimates of how 3D wave focusing and MRI turbulence might alter damping rates, and (iii) states that the reported 2D thresholds should be regarded as a baseline pending future 3D MHD simulations. We do not claim the 2D results are universally definitive. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: claims derived from direct hydrodynamic simulations

full rationale

The paper's central results on relative efficiencies of viscosity, cooling, and nonlinear shock damping are obtained by running a suite of 2D hydrodynamic simulations across ranges of α, β, and q_th, then extracting and comparing radial angular-momentum deposition profiles. No parameter is fitted to a target outcome and then re-labeled as a prediction; no uniqueness theorem or ansatz is imported via self-citation to force the conclusions; and the reported thresholds (e.g., α ≳ 10^{-1.5} for thermal-mass planets) are direct numerical measurements rather than algebraic identities. The derivation chain is therefore self-contained against external benchmarks and receives the default non-circularity score.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The study rests on the standard equations of hydrodynamics with no new free parameters fitted to data and no new entities postulated; the varied quantities α, β, and q_th are input parameters, not derived constants.

assumptions (1)

standard math The disk fluid obeys the standard inviscid or viscous hydrodynamic equations in a rotating frame
Implicit foundation of all protoplanetary-disk simulations described in the abstract.

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Cite this review

Pith. "Pith review of $\alpha\beta q_\mathrm{th}$-mapping of planet-induced density wave damping in protoplanetary discs." pith.science (2026). https://pith.science/paper/56SMOWRR

@misc{pith2026260512607,
  author       = {Pith},
  title        = {Pith review of: $\alpha\beta q_\mathrmth$-mapping of planet-induced density wave damping in protoplanetary discs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/56SMOWRR}},
  note         = {Machine review of arXiv:2605.12607}
}

abstract

Planets embedded in protoplanetary discs are capable of creating a wide variety of substructures through gravitational interactions. This process is mediated through the excitation and damping of density waves which carry angular momentum across the disc. Therefore, to interpret observations of substructures, it is critical to understand the physical processes which lead to deposition of wave angular momentum to the disc fluid. In this study, we explore the relative efficiency of viscosity ($\alpha$), cooling ($\beta$), and non-linear wave evolution ($q_\mathrm{th}$) in damping planet-generated density waves. We run a large suite of hydrodynamic simulations varying viscosity, cooling timescale, and planetary mass, from which we extract radial profiles of wave angular momentum deposition. We quantify the efficiency of different wave damping mechanisms as a joint function of planetary mass, viscosity and cooling time. We find that nonlinear wave evolution leading to shock formation is typically the most important cause of angular momentum deposition, but that cooling on timescales comparable to local orbital time reaches similar levels of importance for low mass planets (sub-thermal, $q_\mathrm{th}<1$). On the contrary, linear wave damping due to viscosity is rather inefficient, requiring $\alpha \gtrsim 10^{-1.5}$ to noticeably affect damping of waves launched by thermal mass planets. Even for lowest mass planets considered ($q_\mathrm{th}=0.025$), viscosity affects wave damping only if $\alpha \gtrsim 10^{-2.9}$. Our findings could be applied to interpret observations of protoplanetary discs; they are also important for understanding wave propagation in other types of astrophysical discs.

Figures

Figures reproduced from arXiv: 2605.12607 by the authors.

**Figure 1.** A representative example of (a) excitation torque density, d𝑇/d𝑅, and (b) angular momentum deposition, d𝐹dep/d𝑅, from isothermal simulations with a 1𝑀th planet (𝑞th = 1), for different values of viscous 𝛼 (indicated in the legend). The observed torque excitation is due to Lindblad resonances and angular momentum deposition is driven essentially by shock dissipation only (the wave shocks first at radii where d𝐹dep/d… view at source ↗

**Figure 2.** Representative radial profiles of (a) torque excitation and (b) angular momentum deposition from inviscid simulations with a 1𝑀th planet (𝑞th = 1), for different values of the cooling timescale 𝛽 (indicated in the legend). Panel (b) also shows (vertical gray lines) the radial extent of the co-orbital region occupied by horseshoe orbits as measured from the 𝛽 = 0 simulations. Changes in cooling timescale modify the … view at source ↗

**Figure 4.** (a) One-sided (𝑇OSL) and (b) total (𝑇) torques compared with linear theory as a function of cooling time 𝛽 and planetary mass 𝑀p (colors, see legend). Linear calculations using the methods of Miranda & Rafikov (2020a) are shown in the gray circles and dashed line. Whilst the linear calculation provides a good estimate of the one-sided torque in the low mass case it fails to accurately predict total torques at high v… view at source ↗

Figures from the paper (6 more)

**Figure 3.** Figure 3: Excitation torque density d𝑇/d𝑅 as a function of planetary mass 𝑀p (colors, shown in legend) and cooling timescale 𝛽 from inviscid simulations and computed using linear theory (black). Note differences from linearity for both the co-rotation torque and overall torque e…

**Figure 5.** Figure 5: Angular momentum deposition d𝐹dep/d𝑅 as a function of planetary mass 𝑀p (or 𝑞th)(rows), cooling time 𝛽 (columns) and viscosity 𝛼 (colours, see legend). The dashed gray line shows the inviscid excitation torque density d𝑇/d𝑅 for each 𝑀p and 𝛽 (viscosity has a weak effec…

**Figure 6.** Figure 6: The normalised difference metric for viscosity 𝜃𝛼 (equation 25) as a function of viscosity 𝛼, planetary mass 𝑀p (or 𝑞th), and a 𝛽-cooling parameter. Line colours illustrate different masses (see legend), and each panel shows results for a different value of 𝛽 (only a s…

**Figure 7.** Figure 7: The normalised difference metric for cooling time-scales: (a, b, c) show the difference of each simulation to the adiabatic case, 𝜃𝛽,adi (Equation 27) and (d, e, f) show the difference metric compared to isothermal simulations, 𝜃𝛽,iso (Equation 26). Each column shows …

**Figure 8.** Figure 8: Contour map of the critical value of 𝛼 below which viscosity can be considered as an unimportant factor in wave damping, as a function of 𝑀p/𝑀th and 𝛽. We define the critical value of 𝛼 based on the condition 𝜃𝛼 (𝛼) = 𝜃crit, with 𝜃𝛼 and 𝜃crit given by equations (25) an…

**Figure 9.** Figure 9: Contour map of the critical values of 𝛽 as a function of planetary mass and viscosity: (a) the critical values of 𝛽 above which the dynamics of wave damping cannot be accurately approximated as isothermal, (b) the critical values of 𝛽 below which wave damping cannot be…

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We explore the relative efficiency of viscosity (α), cooling (β), and non-linear wave evolution (q_th) in damping planet-generated density waves... nonlinear wave evolution leading to shock formation is typically the most important cause...
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We run a large suite of hydrodynamic simulations varying viscosity, cooling timescale, and planetary mass, from which we extract radial profiles of wave angular momentum deposition.

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Works this paper leans on

273 extracted references · 273 canonical work pages

[2]

Angular Momentum Transport and Variability in Boundary Layers of Accretion Disks Driven by Global Acoustic Modes

Angular Momentum Transport and Variability in Boundary Layers of Accretion Disks Driven by Global Acoustic Modes. , keywords =. doi:10.1088/0004-637X/760/1/22 , archivePrefix =. 1205.4009 , primaryClass =

work page Pith review arXiv doi:10.1088/0004-637x/760/1/22
[4]

Optical and Near-infrared View of Planet-forming Disks and Protoplanets

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

work page Pith review doi:10.48550/arxiv.2203.09991 2023
[5]

2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

Non-linear dynamics of the corotation torque. , keywords =. doi:10.1046/j.1365-8711.2001.04619.x , adsurl =

work page doi:10.1046/j.1365-8711.2001.04619.x 2001
[6]

, keywords =

Radiatively Damped Density Waves in Optically Thick Protostellar Disks. , keywords =. doi:10.1086/178107 , adsurl =

work page doi:10.1086/178107
[7]

On the Horseshoe Drag of a Low-Mass Planet. I. Migration in Isothermal Disks. , keywords =. doi:10.1088/0004-637X/703/1/845 , archivePrefix =. 0907.4677 , primaryClass =

work page Pith review arXiv doi:10.1088/0004-637x/703/1/845
[10]

, keywords =

Boundary layers of accretion discs: Discovery of vortex-driven modes and other waves. , keywords =. doi:10.1093/mnras/stab2962 , archivePrefix =. 2103.12119 , primaryClass =

work page doi:10.1093/mnras/stab2962
[11]

, keywords =

Boundary layers of accretion discs: wave-driven transport and disc evolution. , keywords =. doi:10.1093/mnras/stac732 , archivePrefix =. 2111.03068 , primaryClass =

work page doi:10.1093/mnras/stac732
[12]

J., & Rafikov, R

Early stages of gap opening by planets in protoplanetary discs. , keywords =. doi:10.1093/mnras/stae2089 , archivePrefix =. 2407.01728 , primaryClass =

work page doi:10.1093/mnras/stae2089

Show all 273 references

[13]

The Open Journal of Astrophysics , keywords =

On inertial forces (indirect terms) in problems with a central body. The Open Journal of Astrophysics , keywords =. doi:10.33232/001c.141682 , archivePrefix =. 2506.23331 , primaryClass =

doi
[14]

, keywords =

Vortex generation in protoplanetary disks with an embedded giant planet. , keywords =. doi:10.1051/0004-6361:20077169 , archivePrefix =. 0706.3200 , primaryClass =

doi arXiv
[15]

, keywords =

The Effects of Cooling on Boundary Layer Accretion. , keywords =. doi:10.3847/1538-4357/ad6d6b , archivePrefix =. 2405.20367 , primaryClass =

doi
[18]

arXiv e-prints , keywords =

Spiral Density Waves and Torque Balance in the Kerr Geometry. arXiv e-prints , keywords =. doi:10.48550/arXiv.2601.19123 , archivePrefix =. 2601.19123 , primaryClass =

doi
[20]

, keywords =

Eccentric planet-disc interactions: orbital migration and eccentricity evolution. , keywords =. doi:10.1093/mnras/staf117 , archivePrefix =. 2407.20398 , primaryClass =

doi
[21]

, keywords =

Weak Turbulence in the HD 163296 Protoplanetary Disk Revealed by ALMA CO Observations. , keywords =. doi:10.1088/0004-637X/813/2/99 , archivePrefix =. 1510.01375 , primaryClass =

doi arXiv
[22]

, keywords =

A Three-dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk Using DCO ^ +. , keywords =. doi:10.3847/1538-4357/aa79f9 , archivePrefix =. 1706.04504 , primaryClass =

doi arXiv
[23]

, keywords =

Inferring Planet Mass from Spiral Structures in Protoplanetary Disks. , keywords =. doi:10.1088/2041-8205/815/2/L21 , archivePrefix =. 1511.01178 , primaryClass =

doi arXiv
[28]

, keywords =

The role of dissipation in shepherding of ring particles. , keywords =. doi:10.1016/0019-1035(83)90142-2 , adsurl =

doi
[29]

Global MHD Simulations of Accretion Disks in Cataclysmic Variables. I. The Importance of Spiral Shocks. , keywords =. doi:10.3847/0004-637X/823/2/81 , archivePrefix =. 1604.00715 , primaryClass =

doi arXiv
[30]

, keywords =

Exploring the formation of multiple dust-trapping rings in the inner Solar System. , keywords =. doi:10.1051/0004-6361/202555284 , archivePrefix =. 2508.02410 , primaryClass =

doi
[31]

, keywords =

Type I Planet Migration in Nearly Laminar Disks. , keywords =. doi:10.1088/0004-637X/690/1/L52 , archivePrefix =. 0812.0586 , primaryClass =

doi arXiv
[33]

On the Tidal Interaction between Protoplanets and the Primordial Solar Nebula. II. Self-Consistent Nonlinear Interaction. , keywords =. doi:10.1086/164426 , adsurl =

doi
[34]

On the Tidal Interaction between Protoplanets and the Protoplanetary Disk. III. Orbital Migration of Protoplanets. , keywords =. doi:10.1086/164653 , adsurl =

doi
[36]

, volume = 875, number = 1, pages = 37, doi =
[38]

, volume = 892, number = 1, pages = 65, doi =
[41]

I - Linear calculation of the role of angular momentum exchange

On the tidal interaction between protoplanets and the primordial solar nebula. I - Linear calculation of the role of angular momentum exchange. , keywords =. doi:10.1086/162561 , adsurl =

doi
[46]

, keywords =

Indirect forces in disc─planet interaction. , keywords =. doi:10.1093/mnras/stag344 , archivePrefix =. 2511.10745 , primaryClass =

doi arXiv
[47]

Observational appearance

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

1973
[49]

, keywords =

Spiral-wave-driven accretion in quiescent dwarf nov. , keywords =. doi:10.1051/0004-6361/202346090 , archivePrefix =. 2304.13773 , primaryClass =

doi
[54]

Astronomy & Astrophysics , author =

Particle dynamics in discs with turbulence generated by the vertical shear instability , volume =. Astronomy & Astrophysics , author =. 2016 , pages =. doi:10.1051/0004-6361/201527716 , urldate =

2016 doi
[55]

Monthly Notices of the Royal Astronomical Society , author =

Magnetic shear-flow instability in thin accretion discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 1999 , pages =. doi:10.1046/j.1365-8711.1999.02577.x , language =

1999 doi
[56]

Astronomy & Astrophysics , author =

Magnetic shear-driven instability and turbulent mixing in magnetized protostellar disks , volume =. Astronomy & Astrophysics , author =. 2008 , pages =. doi:10.1051/0004-6361:20077562 , number =

2008 doi
[57]

2013 , pages =

The Astrophysical Journal , author =. 2013 , pages =. doi:10.1088/0004-637X/769/1/76 , number =

2013 doi
[58]

The Astrophysical Journal , author =

Wind-driven. The Astrophysical Journal , author =. 2013 , note =. doi:10.1088/0004-637X/772/2/96 , abstract =

2013 doi
[59]

Monthly Notices of the Royal Astronomical Society , author =

Protoplanetary disc ‘isochrones’ and the evolution of discs in the. Monthly Notices of the Royal Astronomical Society , author =. 2017 , pages =. doi:10.1093/mnras/stx2273 , language =

2017 doi
[60]

, volume =

The evolution of viscous discs and the origin of the nebular variables. , volume =. Monthly Notices of the Royal Astronomical Society , author =. 1974 , note =. doi:10.1093/mnras/168.3.603 , abstract =

1974 doi
[61]

Qiao, Lin and Coleman, Gavin A. L. and Haworth, Thomas J. , month = mar, year =. Planet formation via pebble accretion in externally photoevaporating discs , url =
[62]

Astronomy & Astrophysics , author =

A spectacular jet from the bright 244-440. Astronomy & Astrophysics , author =. 2023 , note =. doi:10.1051/0004-6361/202245428 , abstract =

2023 doi
[63]

The Astrophysical Journal , author =

Protoplanetary. The Astrophysical Journal , author =. 2017 , pages =. doi:10.3847/1538-4357/aa6249 , number =

2017 doi
[64]

Restrepo, Steven Rendon and Barge, Pierre and Vavrik, Radim , month = mar, year =
[65]

Astronomy & Astrophysics , author =

Separating gas-giant and ice-giant planets by halting pebble accretion , volume =. Astronomy & Astrophysics , author =. 2014 , pages =. doi:10.1051/0004-6361/201423814 , urldate =

2014 doi
[66]

Monthly Notices of the Royal Astronomical Society , author =

A simple time-dependent method for calculating spirals: applications to eccentric planets in protoplanetary discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2022 , pages =. doi:10.1093/mnras/stab3641 , abstract =

2022 doi
[67]

Monthly Notices of the Royal Astronomical Society , author =

Density waves in protoplanetary discs excited by eccentric planets: linear theory , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2022 , pages =. doi:10.1093/mnras/stac2802 , abstract =

2022 doi
[68]

The Astrophysical Journal , author =

Circumplanetary. The Astrophysical Journal , author =. 2019 , pages =. doi:10.3847/1538-4357/ab53da , number =

2019 doi
[69]

The Astrophysical Journal , author =

New. The Astrophysical Journal , author =. 2019 , pages =. doi:10.3847/1538-4357/ab20ce , number =

2019 doi
[70]

The Astrophysical Journal , author =

An. The Astrophysical Journal , author =. 2020 , pages =. doi:10.3847/1538-4357/ab5b0f , number =

2020 doi
[71]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 2018 , pages =. doi:10.3847/2041-8213/aaf747 , number =

2018 doi
[72]

and Fukuhara, S

Komaki, A. and Fukuhara, S. and Suzuki, T. K. and Yoshida, N. , month = apr, year =. Simulations of
[73]

Monthly Notices of the Royal Astronomical Society , author =

Deep and wide gaps by super. Monthly Notices of the Royal Astronomical Society , author =. 2018 , pages =. doi:10.1093/mnras/sty1466 , language =

2018 doi
[74]

, year =

Duffell, Paul C. , year =. A. doi:10.48550/ARXIV.1505.03514 , abstract =

doi arXiv
[75]

Multiple

Yang, Yi and Liu, Hauyu Baobab and Muto, Takayuki and Hashimoto, Jun and Dong, Ruobing and Kanagawa, Kazuhiro and Momose, Munetake and Akiyama, Eiji and Hasegawa, Yasuhiro and Tsukagoshi, Takashi and Konishi, Mihoko and Tamura, Motohide , month = mar, year =. Multiple
[76]

The Astrophysical Journal , author =

What is the. The Astrophysical Journal , author =. 2017 , note =. doi:10.3847/1538-4357/835/2/146 , abstract =

2017 doi
[77]

The Astrophysical Journal , author =

Pileups and. The Astrophysical Journal , author =. 2020 , pages =. doi:10.3847/1538-4357/ab723c , number =

2020 doi
[78]

The Astrophysical Journal , author =

Multiple. The Astrophysical Journal , author =. 2018 , pages =. doi:10.3847/1538-4357/aadadd , number =

2018 doi
[79]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 2018 , note =. doi:10.3847/2041-8213/aaf744 , abstract =

2018 doi
[80]

The Astrophysical Journal , author =

Mapping the. The Astrophysical Journal , author =. 2022 , note =. doi:10.3847/2041-8213/ac64a7 , abstract =

2022 doi
[81]

On the Horseshoe Drag of a Low-Mass Planet. II. Migration in Adiabatic Disks. , keywords =. doi:10.1088/0004-637X/703/1/857 , archivePrefix =. 0907.4676 , primaryClass =

doi arXiv
[82]

The Astrophysical Journal , author =

Multiple. The Astrophysical Journal , author =. 2019 , pages =. doi:10.3847/1538-4357/ab0f9e , number =

2019 doi
[83]

Hu, Xiao and Li, Zhi-Yun and Wang, Lile and Zhu, Zhaohuan and Bae, Jaehan , month = may, year =. Gap
[84]

and Batygin, K

Morbidelli, A. and Batygin, K. and Lega, E. , month = jun, year =. In-situ enrichment in heavy elements of hot
[85]

Monthly Notices of the Royal Astronomical Society , author =

Planet-driven density waves in protoplanetary discs:. Monthly Notices of the Royal Astronomical Society , author =. 2021 , note =. doi:10.1093/mnras/stab2652 , abstract =

2021 doi
[86]

Monthly Notices of the Royal Astronomical Society , author =

Vortex weighing and dating of planets in protoplanetary discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2023 , note =. doi:10.1093/mnras/stac3692 , abstract =

2023 doi
[87]

Monthly Notices of the Royal Astronomical Society , author =

Emergence of vortices at the edges of planet-driven gaps in protoplanetary discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2023 , note =. doi:10.1093/mnras/stac3507 , abstract =

2023 doi
[88]

The interplay between pebble and planetesimal accretion in population synthesis models and its role in giant planet formation , url =

Kessler, Andrin and Alibert, Yann , month = apr, year =. The interplay between pebble and planetesimal accretion in population synthesis models and its role in giant planet formation , url =
[89]

The Astrophysical Journal , author =

Protoplanetary. The Astrophysical Journal , author =. 2016 , note =. doi:10.3847/0004-637X/831/2/122 , abstract =

2016 doi
[90]

Publications of the Astronomical Society of Japan , author =

Mass constraint for a planet in a protoplanetary disk from the gap width , volume =. Publications of the Astronomical Society of Japan , author =. 2016 , note =. doi:10.1093/pasj/psw037 , abstract =

2016 doi
[91]

, month = jan, year =

Armitage, Philip J. , month = jan, year =. Astrophysics of planet formation,
[92]

Annual Review of Astronomy and Astrophysics , author =

Observations of. Annual Review of Astronomy and Astrophysics , author =. 2020 , pages =. doi:10.1146/annurev-astro-031220-010302 , abstract =

2020 doi
[93]

The Astrophysical Journal , author =

The excitation of density waves at the. The Astrophysical Journal , author =. 1979 , note =. doi:10.1086/157448 , abstract =

1979 doi
[94]

The Astrophysical Journal , author =

An. The Astrophysical Journal , author =. 2019 , note =. doi:10.3847/1538-4357/ab2537 , abstract =

2019 doi
[95]

The Astrophysical Journal , author =

Planet. The Astrophysical Journal , author =. 2002 , note =. doi:10.1086/340228 , abstract =

2002 doi
[96]

Monthly Notices of the Royal Astronomical Society , author =

Accretion disc viscosity: how big is alpha? , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2007 , pages =. doi:10.1111/j.1365-2966.2007.11556.x , language =

2007 doi
[97]

Binkert, Fabian , month = jun, year =. Beyond
[98]

The Astrophysical Journal , author =

Radial. The Astrophysical Journal , author =. 2002 , note =. doi:10.1086/344437 , abstract =

2002 doi
[99]

Astronomy & Astrophysics , author =

Pebble isolation mass --- scaling law and implications for the formation of super-. Astronomy & Astrophysics , author =. 2018 , note =. doi:10.1051/0004-6361/201731931 , abstract =

2018 doi
[100]

and Dong, Ruobing and Choquet, Élodie and Vigan, Arthur and Gonzalez, Jean-François and Wagner, Kevin and Fang, Taotao and Ubeira-Gabellini, Maria Giulia , month = jun, year =

Xie, Chen and Ren, Bin B. and Dong, Ruobing and Choquet, Élodie and Vigan, Arthur and Gonzalez, Jean-François and Wagner, Kevin and Fang, Taotao and Ubeira-Gabellini, Maria Giulia , month = jun, year =. Dynamical detection of a companion driving a spiral arm in a protoplanetar...
[101]

On the mass of gas giant planets:

Helled, Ravit , month = jun, year =. On the mass of gas giant planets:
[102]

The Astrophysical Journal , author =

Gaps and. The Astrophysical Journal , author =. 2020 , pages =. doi:10.3847/1538-4357/abbee7 , number =

2020 doi
[103]

and Caselli, Paola and Gong, Munan and Silsbee, Kedron , month = jun, year =

Akimkin, Vitaly and Ivlev, Alexei V. and Caselli, Paola and Gong, Munan and Silsbee, Kedron , month = jun, year =. Coagulation-
[104]

and Harsono, Daniel and Vazan, Allona and Liu, Beibei and Ormel, Chris W

Drazkowska, Joanna and Bitsch, Bertram and Lambrechts, Michiel and Mulders, Gijs D. and Harsono, Daniel and Vazan, Allona and Liu, Beibei and Ormel, Chris W. and Kretke, Katherine and Morbidelli, Alessandro , month = may, year =. Planet
[105]

Astronomy & Astrophysics , author =

Protostellar half-life: new methodology and estimates , volume =. Astronomy & Astrophysics , author =. 2018 , pages =. doi:10.1051/0004-6361/201731584 , abstract =

2018 doi
[106]

Nature , author =

Four annular structures in a protostellar disk less than 500,000 years old , volume =. Nature , author =. 2020 , pages =. doi:10.1038/s41586-020-2779-6 , language =

2020 doi
[107]

and Rosotti, G

Alexander, R. and Rosotti, G. and Armitage, P. J. and Herczeg, G. J. and Manara, C. F. and Tabone, B. , month = jun, year =. The distribution of accretion rates as a diagnostic of protoplanetary disc evolution , url =
[108]

Monthly Notices of the Royal Astronomical Society , author =

Secular evolution of. Monthly Notices of the Royal Astronomical Society , author =. 2022 , pages =. doi:10.1093/mnras/stab3442 , abstract =

2022 doi
[109]

, month = jul, year =

Lesur, G. , month = jul, year =. Magnetohydrodynamics of protoplanetary discs , url =
[110]

2015 , pages =

The Astrophysical Journal , author =. 2015 , pages =. doi:10.1088/0004-637X/802/1/42 , number =

2015 doi
[111]

The Astrophysical Journal , author =

Low-mass. The Astrophysical Journal , author =. 2013 , note =. doi:10.1088/0004-637X/768/2/143 , abstract =

2013 doi
[112]

The Astrophysical Journal , author =

Model of a. The Astrophysical Journal , author =. 2020 , note =. doi:10.3847/1538-4357/ab781e , abstract =

2020 doi
[113]

Monthly Notices of the Royal Astronomical Society , author =

A dusty origin for the correlation between protoplanetary disc accretion rates and dust masses , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2020 , note =. doi:10.1093/mnras/staa2519 , abstract =

2020 doi
[114]

Astronomy & Astrophysics , author =

The. Astronomy & Astrophysics , author =. 2023 , pages =. doi:10.1051/0004-6361/202245637 , abstract =

2023 doi
[115]

Monthly Notices of the Royal Astronomical Society , author =

Modeling planet-induced gaps and rings in. Monthly Notices of the Royal Astronomical Society , author =. 2023 , note =. doi:10.1093/mnras/stad1973 , abstract =

2023 doi
[116]

Monthly Notices of the Royal Astronomical Society , author =

Distinguishing. Monthly Notices of the Royal Astronomical Society , author =. 2023 , note =. doi:10.1093/mnras/stad1553 , abstract =

2023 doi
[117]

2015 , pages =

The Astrophysical Journal , author =. 2015 , pages =. doi:10.1088/2041-8205/808/1/L3 , number =

2015 doi
[118]

Monthly Notices of the Royal Astronomical Society , author =

Connecting. Monthly Notices of the Royal Astronomical Society , author =. 2017 , pages =. doi:10.1093/mnras/stx772 , language =

2017 doi
[119]

The Astrophysical Journal , author =

Dust and. The Astrophysical Journal , author =. 2016 , note =. doi:10.3847/0004-637X/816/1/25 , abstract =

2016 doi
[120]

The Astrophysical Journal Supplement Series , author =

The. The Astrophysical Journal Supplement Series , author =. 2020 , pages =. doi:10.3847/1538-4365/ab929b , number =

2020 doi
[121]

and Rosotti, G

Pizzati, E. and Rosotti, G. P. and Tabone, B. , month = jul, year =. Constraining turbulence in protoplanetary discs using the gap contrast: an application to the
[122]

New Astronomy Reviews , author =

Empirical constraints on turbulence in proto-planetary discs , volume =. New Astronomy Reviews , author =. 2023 , note =. doi:10.1016/j.newar.2023.101674 , abstract =

2023 doi
[123]

The Astrophysical Journal , author =

An analytical model of radial dust trapping in protoplanetary disks , volume =. The Astrophysical Journal , author =. 2019 , note =. doi:10.3847/1538-4357/ab1265 , abstract =

2019 doi
[124]

The Astrophysical Journal Supplement Series , author =

A. The Astrophysical Journal Supplement Series , author =. 2022 , pages =. doi:10.3847/1538-4365/ac76cb , abstract =

2022 doi
[125]

The Astrophysical Journal Supplement Series , author =

An. The Astrophysical Journal Supplement Series , author =. 2020 , pages =. doi:10.3847/1538-4365/ab82ff , number =

2020 doi
[126]

and Nelson, Richard P

Joseph, Jibin and Ziampras, Alexandros and Jordan, Lucas and Turpin, George A. and Nelson, Richard P. , month = aug, year =. Measuring the
[127]

2015 , pages =

The Astrophysical Journal , author =. 2015 , pages =. doi:10.1088/2041-8205/812/2/L38 , number =

2015 doi
[128]

Publications of the Astronomical Society of Japan , author =

Modelling of deep gaps created by giant planets in protoplanetary disks , volume =. Publications of the Astronomical Society of Japan , author =. 2017 , note =. doi:10.1093/pasj/psx114 , abstract =

2017 doi
[129]

2015 , pages =

The Astrophysical Journal , author =. 2015 , pages =. doi:10.1088/2041-8205/806/1/L15 , number =

2015 doi
[130]

The Astrophysical Journal , author =

Imaging the. The Astrophysical Journal , author =. 2020 , pages =. doi:10.3847/1538-4357/abcafc , number =

2020 doi
[131]

and Hosokawa, Takashi and Guedel, Manuel , month = jul, year =

Matsukoba, Ryoki and Vorobyov, Eduard I. and Hosokawa, Takashi and Guedel, Manuel , month = jul, year =. Formation of a wide-orbit giant planet in a gravitationally unstable subsolar-metallicity protoplanetary disc , url =
[132]

and Hinz, Phil and Briesemeister, Zackery and Lawson, Kellen and Ménard, François and Pantin, Eric and Russell, Ray W

Wagner, Kevin and Stone, Jordan and Skemer, Andrew and Ertel, Steve and Dong, Ruobing and Apai, Dániel and Spalding, Eckhart and Leisenring, Jarron and Sitko, Michael and Kratter, Kaitlin and Barman, Travis and Marley, Mark and Miles, Brittany and Boccaletti, Anthony and Assan...
[133]

Liu, Hanpu and Bai, Xue-Ning , month = aug, year =. The
[134]

Formation of inner planets in the presence of a

Guo, Kangrou and Kokubo, Eiichiro , month = aug, year =. Formation of inner planets in the presence of a
[135]

Monthly Notices of the Royal Astronomical Society , author =

Gas pile-up, gap overflow and. Monthly Notices of the Royal Astronomical Society , author =. 2012 , pages =. doi:10.1111/j.1365-2966.2012.22129.x , language =

2012 doi
[136]

2011 , pages =

The Astrophysical Journal , author =. 2011 , pages =. doi:10.1088/0004-637X/739/1/10 , number =

2011 doi
[137]

How to make giant planets via pebble accretion , url =

Savvidou, Sofia and Bitsch, Bertram , month = sep, year =. How to make giant planets via pebble accretion , url =
[138]

Astronomy and Astrophysics , author =

Black holes in binary systems. Astronomy and Astrophysics , author =. 1973 , note =

1973
[139]

The Astrophysical Journal Letters , author =

The time evolution of \. The Astrophysical Journal Letters , author =. 2023 , note =. doi:10.3847/2041-8213/acf048 , abstract =

2023 doi
[140]

and Menard, F

Duchene, G. and Menard, F. and Stapelfeldt, K. and Villenave, M. and Wolff, S. G. and Perrin, M. D. and Pinte, C. and Tazaki, R. and Padgett, D. L. , month = sep, year =
[141]

, month = jun, year =

Balbus, Steven A. , month = jun, year =. Enhanced. doi:10.1146/annurev.astro.41.081401.155207 , abstract =

doi
[142]

Astronomy & Astrophysics , author =

Systematic description of wind-driven protoplanetary discs , volume =. Astronomy & Astrophysics , author =. 2021 , pages =. doi:10.1051/0004-6361/202040109 , abstract =

2021 doi
[143]

Sandwiched planet formation: restricting the mass of a middle planet , shorttitle =

Pritchard, Matthew and Meru, Farzana and Rowther, Sahl and Armstrong, David and Randall, Kaleb , month = oct, year =. Sandwiched planet formation: restricting the mass of a middle planet , shorttitle =
[144]

Monthly Notices of the Royal Astronomical Society , author =

Gap opening by planets in discs with magnetized winds , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2022 , note =. doi:10.1093/mnras/stac1774 , abstract =

2022 doi
[145]

Chen, Kan and Kama, Mihkel and Pinilla, Paola and Keyte, Luke , month = oct, year =. Planet
[146]

The dependence of the structure of planet-opened gaps in protoplanetary disks on radiative cooling , url =

Zhang, Minghao and Huang, Pinghui and Dong, Ruobing , month = oct, year =. The dependence of the structure of planet-opened gaps in protoplanetary disks on radiative cooling , url =
[147]

2022 , pages =

Monthly Notices of the Royal Astronomical Society: Letters , author =. 2022 , pages =. doi:10.1093/mnrasl/slab124 , abstract =

2022 doi
[148]

The Astrophysical Journal , author =

Resolved. The Astrophysical Journal , author =. 2011 , note =. doi:10.1088/0004-637X/732/1/42 , abstract =

2011 doi
[149]

The Astrophysical Journal , author =

Nonlinear. The Astrophysical Journal , author =. 2002 , note =. doi:10.1086/339399 , abstract =

2002 doi
[150]

2020 , pages =

Nature Methods , author =. 2020 , pages =. doi:10.1038/s41592-019-0686-2 , abstract =

2020 doi
[151]

The Astrophysical Journal , author =

Disk. The Astrophysical Journal , author =. 2018 , note =. doi:10.3847/1538-4357/aaa8e8 , abstract =

2018 doi
[152]

2011 , pages =

The Astrophysical Journal , author =. 2011 , pages =. doi:10.1088/0004-637X/741/1/56 , number =

2011 doi
[153]

and Ogilvie, Gordon and Tanaka, Hidekazu , month = mar, year =

Paardekooper, Sijme-Jan and Dong, Ruobing and Duffell, Paul and Fung, Jeffrey and Masset, Frederic S. and Ogilvie, Gordon and Tanaka, Hidekazu , month = mar, year =. Planet-. doi:10.48550/arXiv.2203.09595 , abstract =

doi
[154]

Monthly Notices of the Royal Astronomical Society , author =

The effects of disc self-gravity and radiative cooling on the formation of gaps and spirals by young planets , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2020 , note =. doi:10.1093/mnras/staa404 , abstract =

2020 doi
[155]

Monthly Notices of the Royal Astronomical Society , author =

Using planet migration and dust drift to weigh protoplanetary discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2023 , note =. doi:10.1093/mnras/stad1791 , abstract =

2023 doi
[156]

Icarus , author =

Protoplanet. Icarus , author =. 1997 , note =. doi:10.1006/icar.1996.5647 , abstract =

1997 doi
[157]

Monthly Notices of the Royal Astronomical Society , author =

Estimating the depth of gaps opened by planets in eccentric orbit , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2022 , note =. doi:10.1093/mnras/stac2856 , abstract =

2022 doi
[158]

and Ono, Tomohiro and Momose, Munetake , month = aug, year =

Kanagawa, Kazuhiro D. and Ono, Tomohiro and Momose, Munetake , month = aug, year =. Kinematic signatures of a low-mass planet with a moderately inclined orbit in a protoplanetary disk , url =
[160]

The Astrophysical Journal , author =

Planetary. The Astrophysical Journal , author =. 2001 , note =. doi:10.1086/320572 , abstract =

2001 doi
[161]

The Astrophysical Journal , author =

Gap. The Astrophysical Journal , author =. 2013 , note =. doi:10.1088/0004-637X/769/1/41 , abstract =

2013 doi
[162]

The Astrophysical Journal , author =

Particle. The Astrophysical Journal , author =. 2014 , note =. doi:10.1088/0004-637X/785/2/122 , abstract =

2014 doi
[163]

Saas-Fee Advanced Course , author =

Physical. Saas-Fee Advanced Course , author =. 2019 , note =. doi:10.1007/978-3-662-58687-7_1 , abstract =

2019 doi
[164]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 2015 , note =. doi:10.1088/0004-637X/813/2/88 , abstract =

2015 doi
[165]

The Astrophysical Journal , author =

Planet-driven. The Astrophysical Journal , author =. 2018 , note =. doi:10.3847/1538-4357/aabf8c , abstract =

2018 doi
[166]

and Teague, R

Pinte, C. and Teague, R. and Flaherty, K. and Hall, C. and Facchini, S. and Casassus, S. , month = jul, year =. Kinematic. doi:10.48550/arXiv.2203.09528 , abstract =

doi
[167]

and Rafikov, Roman R

Cimerman, Nicolas P. and Rafikov, Roman R. and Miranda, Ryan , month = jun, year =. Torque wiggles -- a robust feature of the global disc-planet interaction , url =
[168]

The Astrophysical Journal , author =

Rossby. The Astrophysical Journal , author =. 1999 , note =. doi:10.1086/306900 , abstract =

1999 doi
[169]

Monthly Notices of the Royal Astronomical Society , author =

On the wake generated by a planet in a disc , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2002 , note =. doi:10.1046/j.1365-8711.2002.05148.x , abstract =

2002 doi
[170]

The Astrophysical Journal , author =

Tides in. The Astrophysical Journal , author =. 1989 , note =. doi:10.1086/167664 , abstract =

1989 doi
[171]

The Astrophysical Journal , author =

On the planetary interpretation of multiple gaps and rings in protoplanetary disks seen by. The Astrophysical Journal , author =. 2019 , note =. doi:10.3847/2041-8213/ab22a7 , abstract =

2019 doi
[172]

The Astrophysical Journal , author =

Gap. The Astrophysical Journal , author =. 1996 , note =. doi:10.1086/177013 , abstract =

1996 doi
[173]

The Astrophysical Journal , author =

Gap. The Astrophysical Journal , author =. 2003 , note =. doi:10.1086/374409 , abstract =

2003 doi
[174]

The Astrophysical Journal , author =

Global. The Astrophysical Journal , author =. 2012 , note =. doi:10.1088/0004-637X/755/1/7 , abstract =

2012 doi
[175]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 2018 , note =. doi:10.3847/2041-8213/aaf741 , abstract =

2018 doi
[176]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 2018 , note =. doi:10.3847/1538-4357/aac6cb , abstract =

2018 doi
[177]

The Astrophysical Journal , author =

A. The Astrophysical Journal , author =. 1991 , note =. doi:10.1086/170270 , abstract =

1991 doi
[178]

The Astrophysical Journal , author =

Layered. The Astrophysical Journal , author =. 1996 , note =. doi:10.1086/176735 , abstract =

1996 doi
[179]

and Ercolano, B

Lesur, G. and Ercolano, B. and Flock, M. and Lin, M.-K. and Yang, C.-C. and Barranco, J. A. and Benitez-Llambay, P. and Goodman, J. and Johansen, A. and Klahr, H. and Laibe, G. and Lyra, W. and Marcus, P. and Nelson, R. P. and Squire, J. and Simon, J. B. and Turner, N. and Umu...
[180]

The Astrophysical Journal , author =

Long-lived. The Astrophysical Journal , author =. 2017 , pages =. doi:10.3847/1538-4357/835/2/118 , number =

2017 doi
[181]

The Astrophysical Journal , author =

Spiral. The Astrophysical Journal , author =. 2018 , pages =. doi:10.3847/1538-4357/aaccfc , number =

2018 doi
[182]

Monthly Notices of the Royal Astronomical Society , author =

On the vertical-shear instability in astrophysical discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2015 , pages =. doi:10.1093/mnras/stv640 , language =

2015 doi
[183]

, volume =

Tidal torques on accretion discs in binary systems with extreme mass ratios. , volume =. Monthly Notices of the Royal Astronomical Society , author =. 1979 , note =. doi:10.1093/mnras/186.4.799 , abstract =

1979 doi
[184]

, volume =

On the structure of circumbinary accretion disks and the tidal evolution of commensurable satellites. , volume =. Monthly Notices of the Royal Astronomical Society , author =. 1979 , note =. doi:10.1093/mnras/188.2.191 , abstract =

1979 doi
[185]

Monthly Notices of the Royal Astronomical Society , author =

On the structure and evolution of the primordial solar nebula , volume =. Monthly Notices of the Royal Astronomical Society , author =. 1980 , note =. doi:10.1093/mnras/191.1.37 , abstract =

1980 doi
[186]

Lin, D. N. C. and Papaloizou, J. C. B. , month = jan, year =. On the
[187]

The Astrophysical Journal , author =

Three-. The Astrophysical Journal , author =. 2002 , note =. doi:10.1086/324713 , abstract =

2002 doi
[188]

Icarus , author =

On the width and shape of gaps in protoplanetary disks , volume =. Icarus , author =. 2006 , note =. doi:10.1016/j.icarus.2005.10.007 , abstract =

2006 doi
[189]

The Astrophysical Journal Supplement Series , author =

A. The Astrophysical Journal Supplement Series , author =. 1996 , note =. doi:10.1086/192311 , abstract =

1996 doi
[190]

The Astrophysical Journal , author =

Three-dimensional. The Astrophysical Journal , author =. 1998 , note =. doi:10.1086/306104 , abstract =

1998 doi
[191]

Astronomy & Astrophysics , author =

Growing and moving low-mass planets in non-isothermal disks , volume =. Astronomy & Astrophysics , author =. 2008 , pages =. doi:10.1051/0004-6361:20078592 , number =

2008 doi
[192]

2011 , pages =

The Astrophysical Journal , author =. 2011 , pages =. doi:10.1088/0004-637X/741/1/57 , number =

2011 doi
[193]

Science , author =

Optical. Science , author =. 2008 , note =. doi:10.1126/science.1166609 , abstract =

2008 doi
[194]

2014 , pages =

The Astrophysical Journal , author =. 2014 , pages =. doi:10.1088/0004-637X/782/2/88 , number =

2014 doi
[195]

The Astrophysical Journal , author =

Transitional. The Astrophysical Journal , author =. 2011 , note =. doi:10.1088/0004-637X/738/2/131 , abstract =

2011 doi
[196]

and Crida, A

Baruteau, C. and Crida, A. and Paardekooper, S. -J. and Masset, F. and Guilet, J. and Bitsch, B. and Nelson, R. and Kley, W. and Papaloizou, J. , month = jan, year =. Planet-. doi:10.2458/azu_uapress_9780816531240-ch029 , note =

doi
[197]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 2012 , note =. doi:10.1088/0004-637X/747/1/24 , abstract =

2012 doi
[198]

Icarus , author =

Formation of the galilean satellites in a gaseous nebula , volume =. Icarus , author =. 1982 , pages =. doi:10.1016/0019-1035(82)90166-X , language =

1982 doi
[199]

2015 , pages =

The Astrophysical Journal , author =. 2015 , pages =. doi:10.1088/2041-8205/809/1/L5 , number =

2015 doi
[200]

The Astrophysical Journal , author =

Gap. The Astrophysical Journal , author =. 2016 , note =. doi:10.3847/0004-637X/832/2/105 , abstract =

2016 doi
[201]

The Astrophysical Journal , author =

Secular. The Astrophysical Journal , author =. 2001 , note =. doi:10.1086/322493 , abstract =

2001 doi
[202]

2016 , note =

The Astrophysical Journal , author =. 2016 , note =. doi:10.3847/2041-8205/819/1/L7 , abstract =

2016 doi
[203]

Monthly Notices of the Royal Astronomical Society , author =

Gap formation by inclined massive planets in locally isothermal three-dimensional discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2017 , note =. doi:10.1093/mnras/stx817 , abstract =

2017 doi
[204]

Icarus , author =

Runaway gas accretion and gap opening versus type. Icarus , author =. 2017 , note =. doi:10.1016/j.icarus.2016.10.017 , abstract =

2017 doi
[205]

Progress of Theoretical Physics Supplement , author =

Structure of the. Progress of Theoretical Physics Supplement , author =. 1981 , note =. doi:10.1143/PTPS.70.35 , abstract =

1981 doi
[206]

Astronomy & Astrophysics , author =

Planets opening dust gaps in gas disks , volume =. Astronomy & Astrophysics , author =. 2004 , pages =. doi:10.1051/0004-6361:200400053 , number =

2004 doi
[207]

Monthly Notices of the Royal Astronomical Society , author =

Type. Monthly Notices of the Royal Astronomical Society , author =. 2010 , note =. doi:10.1111/j.1365-2966.2010.16560.x , abstract =

2010 doi
[208]

The Astrophysical Journal , author =

Disk-. The Astrophysical Journal , author =. 2012 , note =. doi:10.1088/0004-637X/758/1/33 , abstract =

2012 doi
[209]

Monthly Notices of the Royal Astronomical Society , author =

Physics of modes in a differentially rotating system - analysis of the shearing sheet , volume =. Monthly Notices of the Royal Astronomical Society , author =. 1987 , pages =. doi:10.1093/mnras/228.1.1 , language =

1987 doi
[210]

Monthly Notices of the Royal Astronomical Society , author =

Low-mass planet migration in three-dimensional wind-driven inviscid discs: a negative corotation torque , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2020 , pages =. doi:10.1093/mnras/staa576 , abstract =

2020 doi
[211]

The Astrophysical Journal , author =

Planet-driven. The Astrophysical Journal , author =. 2018 , note =. doi:10.3847/1538-4357/aabf93 , abstract =

2018 doi
[212]

The Astrophysical Journal , author =

On the. The Astrophysical Journal , author =. 2017 , pages =. doi:10.3847/1538-4357/aa9705 , number =

2017 doi
[214]

Astronomy & Astrophysics , author =

The impact of planet wakes on the location and shape of the water ice line in a protoplanetary disk , volume =. Astronomy & Astrophysics , author =. 2020 , pages =. doi:10.1051/0004-6361/201936495 , abstract =

2020 doi
[215]

The Astrophysical Journal , author =

Termination of. The Astrophysical Journal , author =. 2019 , pages =. doi:10.3847/2041-8213/ab2a0f , number =

2019 doi
[216]

Monthly Notices of the Royal Astronomical Society , author =

Intermittent planet migration and the formation of multiple dust rings and gaps in protoplanetary discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2020 , pages =. doi:10.1093/mnras/staa379 , abstract =

2020 doi
[217]

The Astrophysical Journal , author =

Angular. The Astrophysical Journal , author =. 2013 , note =. doi:10.1088/0004-637X/770/1/67 , abstract =

2013 doi
[218]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 2018 , note =. doi:10.3847/2041-8213/aaf742 , abstract =

2018 doi
[219]

and Isella, A

Bae, J. and Isella, A. and Zhu, Z. and Martin, R. and Okuzumi, S. and Suriano, S. , month = jul, year =. Structured
[220]

Astronomy & Astrophysics , author =

The. Astronomy & Astrophysics , author =. 2021 , pages =. doi:10.1051/0004-6361/202038553 , abstract =

2021 doi
[221]

The Astrophysical Journal , author =

Two-dimensional. The Astrophysical Journal , author =. 2010 , note =. doi:10.1088/0004-637X/724/1/448 , abstract =

2010 doi
[222]

Physico-chemical

Woitke, Peter , month = dec, year =. Physico-chemical
[223]

Monthly Notices of the Royal Astronomical Society , author =

Formation of a disc gap induced by a planet: effect of the deviation from. Monthly Notices of the Royal Astronomical Society , author =. 2015 , pages =. doi:10.1093/mnras/stv025 , language =

2015 doi
[224]

The Astrophysical Journal , author =

On the. The Astrophysical Journal , author =. 1999 , pages =. doi:10.1086/307594 , language =

1999 doi
[225]

The Astrophysical Journal , author =

On. The Astrophysical Journal , author =. 1990 , note =. doi:10.1086/169277 , abstract =

1990 doi
[226]

Annual Review of Astronomy and Astrophysics , author =

Accretion. Annual Review of Astronomy and Astrophysics , author =. 1981 , pages =. doi:10.1146/annurev.aa.19.090181.001033 , language =

1981 doi
[227]

Can the giant planets of the

Lau, Tommy Chi Ho and Lee, Man Hoi and Brasser, Ramon and Matsumura, Soko , month = jan, year =. Can the giant planets of the
[228]

Earths are not

Xu, Wenrui and Wang, Songhu , month = jan, year =. Earths are not
[229]

The Astrophysical Journal , author =

Architecture of. The Astrophysical Journal , author =. 2020 , pages =. doi:10.3847/1538-4357/ab781b , abstract =

2020 doi
[230]

Nature , author =

Array programming with. Nature , author =. 2020 , pages =. doi:10.1038/s41586-020-2649-2 , abstract =

2020 doi
[231]

Seppänen and hannah and Jae-Joon Lee and Darren Dale and Damon McDougall and Andrew Straw and Paul Hobson and Greg Lucas and Ruth Comer and Christoph Gohlke and Adrien F

Thomas A Caswell and Elliott Sales de Andrade and Antony Lee and Michael Droettboom and Tim Hoffmann and Jody Klymak and John Hunter and Eric Firing and David Stansby and Nelle Varoquaux and Jens Hedegaard Nielsen and Oscar Gustafsson and Kyle Sunden and Benjamin Root and Ryan...
[232]

Icarus , author =

Evolution of grains in a turbulent solar nebula , volume =. Icarus , author =. 1984 , note =. doi:10.1016/0019-1035(84)90164-7 , abstract =

1984 doi
[233]

, volume =

Aerodynamics of solid bodies in the solar nebula. , volume =. Monthly Notices of the Royal Astronomical Society , author =. 1977 , note =. doi:10.1093/mnras/180.2.57 , abstract =

1977 doi
[234]

and Bae, Jaehan and Benisty, Myriam and Bergin, Edwin A

Disk Dynamics Collaboration and Armitage, Philip J. and Bae, Jaehan and Benisty, Myriam and Bergin, Edwin A. and Casassus, Simon and Czekala, Ian and Facchini, Stefano and Fung, Jeffrey and Hall, Cassandra and Ilee, John D. and Keppler, Miriam and Kuznetsova, Aleksandra and Ga...
[235]

Astronomy & Astrophysics , author =

Importance of radiative effects in gap opening by planets in protoplanetary disks , volume =. Astronomy & Astrophysics , author =. 2020 , pages =. doi:10.1051/0004-6361/201937048 , abstract =

2020 doi
[236]

Astronomy & Astrophysics , author =

How cooling influences circumbinary discs , volume =. Astronomy & Astrophysics , author =. 2022 , pages =. doi:10.1051/0004-6361/202243472 , abstract =

2022 doi
[237]

The Astrophysical Journal Letters , author =

Outward. The Astrophysical Journal Letters , author =. 2021 , pages =. doi:10.3847/2041-8213/ac22af , abstract =

2021 doi
[238]

The Astrophysical Journal , author =

Ring. The Astrophysical Journal , author =. 2021 , note =. doi:10.3847/1538-4357/abe1b6 , abstract =

2021 doi
[239]

The Astrophysical Journal , author =

Protoplanetary. The Astrophysical Journal , author =. 2019 , note =. doi:10.3847/1538-4357/aafd31 , abstract =

2019 doi
[240]

and Ogilvie, Gordon I

Latter, Henrik N. and Ogilvie, Gordon I. and Rein, Hanno , month = mar, year =. Planetary rings and other astrophysical disks , url =. doi:10.1017/9781316286791.020 , note =

doi
[241]

and Paardekooper, Sijme-Jan , month = jan, year =

Ziampras, Alexandros and Nelson, Richard P. and Paardekooper, Sijme-Jan , month = jan, year =. Migration of low-mass planets in inviscid disks: the effect of radiation transport on the dynamical corotation torque , shorttitle =
[242]

and Dittmann, Alexander J

Duffell, Paul C. and Dittmann, Alexander J. and D'Orazio, Daniel J. and Franchini, Alessia and Kratter, Kaitlin M. and Penzlin, Anna B. T. and Ragusa, Enrico and Siwek, Magdalena and Tiede, Christopher and Wang, Haiyang and Zrake, Jonathan and Dempsey, Adam M. and Haiman, Zolt...
[243]

and Picogna, Giovanni and Ercolano, Barbara , month = feb, year =

Weber, Michael L. and Picogna, Giovanni and Ercolano, Barbara , month = feb, year =. The interplay between forming planets and photoevaporating discs
[244]

2024 , note =

Astronomy & Astrophysics , author =. 2024 , note =. doi:10.1051/0004-6361/202348421 , abstract =

2024 doi
[245]

Astronomy & Astrophysics , author =

The. Astronomy & Astrophysics , author =. 2021 , pages =. doi:10.1051/0004-6361/202140779 , abstract =

2021 doi
[246]

and Owen, James E

Robinson, Alfie and Booth, Richard A. and Owen, James E. , month = feb, year =. Introducing
[247]

The Astrophysical Journal , author =

Rapid. The Astrophysical Journal , author =. 2021 , pages =. doi:10.3847/1538-4357/abfaa4 , abstract =

2021 doi
[248]

Torii, Naoya and Ida, Shigeru and Kokubo, Eiichiro and Michikoshi, Shugo , month = mar, year =. Global
[249]

, month = mar, year =

Pierens, Arnaud and Nelson, Richard P. , month = mar, year =. Thermal structure of circumbinary discs:
[250]

, month = mar, year =

Helled, Ravit and Stevenson, David J. , month = mar, year =. The fuzzy cores of
[251]

Reviews of Modern Physics , author =

Instability, turbulence, and enhanced transport in accretion disks , volume =. Reviews of Modern Physics , author =. 1998 , pages =. doi:10.1103/RevModPhys.70.1 , language =

1998 doi
[252]

Lin, C. C. and Shu, F. H. , month = jan, year =. Density waves in disk galaxies. , volume =
[253]

1966 , pages =

Proceedings of the National Academy of Sciences , author =. 1966 , pages =. doi:10.1073/pnas.55.2.229 , language =

1966 doi
[254]

The Astrophysical Journal , author =

On the. The Astrophysical Journal , author =. 1964 , note =. doi:10.1086/147955 , abstract =

1964 doi
[255]

, volume =

On the gravitational stability of a disk of stars. , volume =. The Astrophysical Journal , author =. 1964 , note =. doi:10.1086/147861 , abstract =

1964 doi
[256]

Stockholms Observatoriums Annaler , author =

On the possibility of a quasi-stationary spiral structure in galaxies , volume =. Stockholms Observatoriums Annaler , author =. 1963 , note =

1963
[257]

, volume =

Disk-satellite interactions. , volume =. The Astrophysical Journal , author =. 1980 , note =. doi:10.1086/158356 , abstract =

1980 doi
[258]

Monthly Notices of the Royal Astronomical Society , author =

On the. Monthly Notices of the Royal Astronomical Society , author =. 1972 , pages =. doi:10.1093/mnras/157.1.1 , language =

1972 doi
[259]

and Lesur, G

Mauxion, J. and Lesur, G. and Maret, S. , month = mar, year =. Modeling the secular evolution of embedded protoplanetary discs , url =
[260]

Chambers, John , month = mar, year =. Large
[261]

Monthly Notices of the Royal Astronomical Society , author =

The newborn planet population emerging from ring-like structures in discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2019 , pages =. doi:10.1093/mnras/stz913 , language =

2019 doi
[262]

Monthly Notices of the Royal Astronomical Society , author =

The minimum mass of detectable planets in protoplanetary discs and the derivation of planetary masses from high-resolution observations , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2016 , note =. doi:10.1093/mnras/stw691 , abstract =

2016 doi
[263]

The Astrophysical Journal , author =

Using. The Astrophysical Journal , author =. 2022 , pages =. doi:10.3847/1538-4357/ac7a3c , abstract =

2022 doi
[264]

Laune, J. T. and Li, Rixin and Lai, Dong , month = apr, year =. Migration of
[265]

The Astrophysical Journal Supplement Series , author =

The. The Astrophysical Journal Supplement Series , author =. 2010 , note =. doi:10.1088/0067-0049/188/1/290 , abstract =

2010 doi
[266]

Astronomy & Astrophysics , author =

Millimeter emission in photoevaporating disks is determined by early substructures , volume =. Astronomy & Astrophysics , author =. 2023 , pages =. doi:10.1051/0004-6361/202244436 , abstract =

2023 doi
[267]

Meredith and Simon, Jacob B

Flaherty, Kevin and Hughes, A. Meredith and Simon, Jacob B. and Reina, Alicia Smith and Qi, Chunhua and Bai, Xue-Ning and Andrews, Sean M. and Wilner, David J. and Kospal, Agnes , month = jun, year =. Evidence for
[268]

The Astrophysical Journal Letters , author =

The. The Astrophysical Journal Letters , author =. 2018 , pages =. doi:10.3847/2041-8213/aaf740 , abstract =

2018 doi
[269]

There is no disk mass budget problem of planet formation , url =

Savvidou, Sofia and Bitsch, Bertram , month = jul, year =. There is no disk mass budget problem of planet formation , url =
[270]

, month = jul, year =

Chang, Eonho and Youdin, Andrew N. , month = jul, year =. "
[271]

Shoulder of

Bi, Jiaqing and Lin, Min-Kai , month = jun, year =. Shoulder of
[272]

Can gap-edge illumination excite spirals in protoplanetary disks?

Muley, Dhruv and Fuksman, Julio David Melon and Klahr, Hubert , month = aug, year =. Can gap-edge illumination excite spirals in protoplanetary disks?
[273]

Monthly Notices of the Royal Astronomical Society , author =

Horseshoes and spiral waves: capturing the. Monthly Notices of the Royal Astronomical Society , author =. 2024 , note =. doi:10.1093/mnras/stae2060 , abstract =

2024 doi
[274]

The Astrophysical Journal , author =

Three-dimensional. The Astrophysical Journal , author =. 2024 , note =. doi:10.3847/1538-4357/ad410d , abstract =

2024 doi
[275]

Monthly Notices of the Royal Astronomical Society , author =

Dynamics of cold circumstellar gas in debris discs , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2024 , pages =. doi:10.1093/mnras/stae924 , abstract =

2024 doi
[276]

and Kral, Q

Bergez-Casalou, C. and Kral, Q. , month = nov, year =. Observing planetary gaps in the gas of debris disks , url =. doi:10.48550/arXiv.2411.14241 , abstract =

doi
[277]

Modeling protoplanetary disk heating by planet-induced spiral shocks , url =

Ono, Tomohiro and Okamura, Tatsuki and Okuzumi, Satoshi and Muto, Takayuki , month = nov, year =. Modeling protoplanetary disk heating by planet-induced spiral shocks , url =. doi:10.48550/arXiv.2411.09940 , abstract =

doi
[278]

Earth and Planetary Science Letters , author =

Did the terrestrial planets of the solar system form by pebble accretion? , volume =. Earth and Planetary Science Letters , author =. 2025 , pages =. doi:10.1016/j.epsl.2024.119120 , language =

2025 doi
[279]

, month = dec, year =

Armitage, Philip J. , month = dec, year =. Planet formation theory: an overview , shorttitle =. doi:10.48550/arXiv.2412.11064 , abstract =

doi
[280]

The Astrophysical Journal , author =

Water. The Astrophysical Journal , author =. 2024 , note =. doi:10.3847/1538-4357/ad891d , abstract =

2024 doi
[281]

Ma, Xiaoyi and Huang, Pinghui and Yu, Cong and Dong, Ruobing , month = dec, year =. Vortex-. doi:10.48550/arXiv.2412.11507 , abstract =

doi
[282]

and Marino, S

Matrà, L. and Marino, S. and Wilner, D. J. and Kennedy, G. M. and Booth, M. and Krivov, A. V. and Williams, J. P. and Hughes, A. M. and Burgo, C. del and Carpenter, J. and Davies, C. L. and Ertel, S. and Kral, Q. and Lestrade, J.-F. and Marshall, J. P. and Milli, J. and Öberg,...

doi
[283]

The Astrophysical Journal , author =

Three-dimensional. The Astrophysical Journal , author =. 2023 , pages =. doi:10.3847/1538-4357/acb81f , abstract =

2023 doi
[284]

Astronomy & Astrophysics , author =

Effect of wind-driven accretion on planetary migration , volume =. Astronomy & Astrophysics , author =. 2020 , pages =. doi:10.1051/0004-6361/201936412 , abstract =

2020 doi
[285]

and Owen, James E

Cummins, Daniel P. and Owen, James E. , month = jan, year =. The. doi:10.48550/arXiv.2409.05951 , abstract =

doi
[286]

Monthly Notices of the Royal Astronomical Society , author =

A comparative study of disc-planet interaction , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2006 , pages =. doi:10.1111/j.1365-2966.2006.10488.x , language =

2006 doi
[287]

Magnetic disk winds in protoplanetary disks:

Kadam, Kundan and Vorobyov, Eduard and Woitke, Peter and Basu, Shantanu and Terwisga, Sierk van , month = feb, year =. Magnetic disk winds in protoplanetary disks:. doi:10.48550/arXiv.2502.00161 , abstract =

doi
[288]

Monthly Notices of the Royal Astronomical Society , author =

Dynamical corotation torques on low-mass planets , volume =. Monthly Notices of the Royal Astronomical Society , author =. 2014 , pages =. doi:10.1093/mnras/stu1542 , language =

2014 doi
[289]

The Astrophysical Journal , author =

Type. The Astrophysical Journal , author =. 2008 , pages =. doi:10.1086/529487 , language =

2008 doi
[290]

Astronomy & Astrophysics , author =

Migration of massive planets in accreting disks , volume =. Astronomy & Astrophysics , author =. 2015 , pages =. doi:10.1051/0004-6361/201424837 , urldate =

2015 doi
[291]

, month = jan, year =

Cuello, Nicolás and Alaguero, Antoine and Poblete, Pedro P. , month = jan, year =. Circumstellar and circumbinary discs in multiple stellar systems , url =. doi:10.48550/arXiv.2501.19249 , abstract =

doi
[292]

Monthly Notices of the Royal Astronomical Society , author =

The theory of kinks --. Monthly Notices of the Royal Astronomical Society , author =. 2021 , note =. doi:10.1093/mnras/stab1145 , abstract =

2021 doi
[293]

The Astrophysical Journal , author =

The. The Astrophysical Journal , author =. 2024 , pages =. doi:10.3847/1538-4357/ad055c , abstract =

2024 doi
[294]

Astronomy & Astrophysics , author =

Dust ring and gap formation by gas flow induced by low-mass planets embedded in protoplanetary disks:. Astronomy & Astrophysics , author =. 2024 , pages =. doi:10.1051/0004-6361/202451159 , abstract =

2024 doi
[295]

and Rosotti, Giovanni P

Bae, Jaehan and Flock, Mario and Izquierdo, Andres and Kanagawa, Kazuhiro and Ono, Tomohiro and Pinte, Christophe and Price, Daniel J. and Rosotti, Giovanni P. and Wafflard-Fernandez, Gaylor and Lesur, Geoffroy and Masset, Frederic and Andrews, Sean M. and Barrasa-Alfaro, Marc...

doi
[296]

The Astrophysical Journal , author =

Mind the. The Astrophysical Journal , author =. 2024 , pages =. doi:10.3847/1538-4357/ad83d0 , abstract =

2024 doi
[297]

Soto, Arturo Cevallos and Zhu, Zhaohuan , month = may, year =. Young. doi:10.48550/arXiv.2505.03701 , abstract =

doi
[298]

, month = may, year =

Constantinou, Tereza and Shorttle, Oliver and Cranmer, Miles and Rimmer, Paul B. , month = may, year =. Comparative. doi:10.48550/arXiv.2505.01512 , abstract =

doi
[299]

The Astrophysical Journal , author =

Circumbinary. The Astrophysical Journal , author =. 2020 , pages =. doi:10.3847/1538-4357/abab95 , abstract =

2020 doi
[300]

Publications of the Astronomical Society of Japan , author =

Wave. Publications of the Astronomical Society of Japan , author =. 1998 , note =. doi:10.1093/pasj/50.1.141 , abstract =

1998 doi

Pith tools

Reviewed May 14, 2026 · model on record in the stance chip above.

[1] [2]

Angular Momentum Transport and Variability in Boundary Layers of Accretion Disks Driven by Global Acoustic Modes

Angular Momentum Transport and Variability in Boundary Layers of Accretion Disks Driven by Global Acoustic Modes. , keywords =. doi:10.1088/0004-637X/760/1/22 , archivePrefix =. 1205.4009 , primaryClass =

work page Pith review arXiv doi:10.1088/0004-637x/760/1/22

[2] [4]

Optical and Near-infrared View of Planet-forming Disks and Protoplanets

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

work page Pith review doi:10.48550/arxiv.2203.09991 2023

[3] [5]

2001, MNRAS, 322, 231, doi: 10.1046/j.1365-8711.2001.04022.x

Non-linear dynamics of the corotation torque. , keywords =. doi:10.1046/j.1365-8711.2001.04619.x , adsurl =

work page doi:10.1046/j.1365-8711.2001.04619.x 2001

[4] [6]

, keywords =

Radiatively Damped Density Waves in Optically Thick Protostellar Disks. , keywords =. doi:10.1086/178107 , adsurl =

work page doi:10.1086/178107

[5] [7]

On the Horseshoe Drag of a Low-Mass Planet. I. Migration in Isothermal Disks. , keywords =. doi:10.1088/0004-637X/703/1/845 , archivePrefix =. 0907.4677 , primaryClass =

work page Pith review arXiv doi:10.1088/0004-637x/703/1/845

[6] [10]

, keywords =

Boundary layers of accretion discs: Discovery of vortex-driven modes and other waves. , keywords =. doi:10.1093/mnras/stab2962 , archivePrefix =. 2103.12119 , primaryClass =

work page doi:10.1093/mnras/stab2962

[7] [11]

, keywords =

Boundary layers of accretion discs: wave-driven transport and disc evolution. , keywords =. doi:10.1093/mnras/stac732 , archivePrefix =. 2111.03068 , primaryClass =

work page doi:10.1093/mnras/stac732

[8] [12]

J., & Rafikov, R

Early stages of gap opening by planets in protoplanetary discs. , keywords =. doi:10.1093/mnras/stae2089 , archivePrefix =. 2407.01728 , primaryClass =

work page doi:10.1093/mnras/stae2089