Pith. sign in

REVIEW 3 major objections 4 minor 68 references

Effects of Thermodynamics on the Concurrent Accretion and Migration of Gas Giants in Protoplanetary Disks

T0 review · 3 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read Efficient cooling makes an accreting gas giant migrate outward; slow cooling makes it migrate inward, with the switch at β≈1.

desk verdict A solid parameter study of accretion and migration with beta-cooling, but the headline beta~1 transition is not yet robust because torque convergence is unverified and the beta grid is coarse. read the letter →

arxiv 2501.15874 v1 pith:7JDYS3AH submitted 2025-01-27 astro-ph.EP

Hening Wu , Ya-ping Li This is my paper · ORCID
classification astro-ph.EP
keywords protoplanetarydisksplanetmigrationcircumplanetarydiskplanetaryaccretionbeta-coolingprescriptiongasgiantformationplanet-diskinteraction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish that the thermodynamic state of the gas around an accreting giant planet—specifically how rapidly it can cool—controls whether the planet migrates inward or outward while it is still growing. In 2D global hydrodynamic simulations of a Jupiter-mass planet in a protoplanetary disk, the authors vary a single thermal-relaxation timescale and find that efficient cooling produces a rotationally supported, asymmetric circumplanetary disk whose positive torque pushes the planet outward, whereas slow cooling makes the circumplanetary envelope nearly symmetric and lets the negative torque from the outer disk pull the planet inward. The switch occurs near the point where the cooling timescale equals the local dynamical timescale ($\beta \sim 1$). A sympathetic reader would care because migration direction decides where gas giants end up, and the result says that local disk cooling—not just planet mass and disk viscosity—can determine that final orbit. It also gives a concrete target for radiative-hydrodynamic simulations to confirm or refute.

What carries the argument

The central object is the circumplanetary disk (CPD), the gas structure inside the planet's Hill sphere, whose azimuthal asymmetry sets the sign of the gravitational torque. The paper controls thermodynamics with a $\beta$-cooling prescription in which the internal energy relaxes toward its initial profile on a timescale $\beta/\Omega$, with $\Omega$ the local Keplerian frequency; low $\beta$ approaches the isothermal limit and high $\beta$ approaches the adiabatic limit. The load-bearing diagnostic is the spatial asymmetry of the gravitational torque, $\Gamma(r,\phi)+\Gamma(r,-\phi)$, integrated within the Hill sphere: efficient cooling leaves a prograde, asymmetric CPD with a net positive torque, while slow cooling replaces it with a nearly isotropic, pressure-supported envelope whose positive torque vanishes and whose flow can even become retrograde.

What would settle it

Run a radiative-hydrodynamic simulation of an accreting Jupiter-mass planet with wavelength-dependent cooling and measure the torque inside one Hill radius; if a rotationally supported, asymmetric circumplanetary disk—and its associated positive torque—survives even when the effective cooling time exceeds the local orbital time, the $\beta \approx 1$ migration transition predicted here is an artifact of the cooling prescription.

Watch

Extended reading notes

Core claim

The central claim is that for an accreting Jupiter-mass planet on a circular orbit in a viscous protoplanetary disk, the direction of migration is set by the cooling timescale of gas inside the planet's Hill sphere. In the isothermal limit and for $\beta \lesssim 0.1$, the gas forms a rotationally supported, nearly Keplerian circumplanetary disk whose density and torque distributions are asymmetric: the leading side exerts a stronger positive torque than the trailing side exerts negative torque, and this positive contribution overcomes the negative differential Lindblad torque from the outer disk, so the planet migrates outward. As the cooling timescale lengthens, the circumplanetary disk shrinks and becomes less rotationally supported; at $\beta \gtrsim 10$ it is replaced by a pressure-supported, more spherical envelope whose rotation can even become retrograde, the torque asymmetry nearly vanishes, and the planet migrates inward. The total torque crosses zero around $\beta \sim 1$, when the cooling time is comparable to the local dynamical time. The paper also reports a mild decline in the planetary accretion rate with increasing $\beta$, with accretion still limited by the mass supply from the outer disk and driven chiefly by spiral-shock (Reynolds) stress in the circumplanetary region.

Load-bearing premise

The results depend on the assumption that one single cooling timescale, set by the parameter $\beta$, faithfully represents how the gas around the planet loses heat; if real cooling inside the planet's Hill sphere differs from this simple relaxation, the predicted switch near $\beta \approx 1$ could shift or disappear.

Editorial extensions

If this is right

  • In disk regions where the local cooling time is shorter than the orbital time, an accreting Jupiter-mass planet should migrate outward, so efficient cooling changes the expected final orbital radius.
  • Where cooling is slow ($\beta \gtrsim 10$), the same planet migrates inward at a rate roughly three times slower than the classical type I/II estimate for a non-accreting planet.
  • Long cooling timescales also reduce the planet's accretion rate slightly and can drive the circumplanetary gas into retrograde rotation, which would alter how regular satellites form around the planet.
  • Because migration torque depends on thermodynamics, population-synthesis models of gas giants need to include local cooling conditions, not just disk mass and viscosity, to predict where planets park.

Reading between the lines

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

  • If the $\beta \sim 1$ transition holds under more realistic radiative transfer, then a single disk could drive the same planet outward in its outer, efficiently cooling region and inward in its inner, slowly cooling region, suggesting a thermodynamic channel for parking gas giants at intermediate or large radii.
  • The retrograde circumplanetary flow seen at $\beta \gtrsim 10$ implies a thermodynamic criterion for satellite formation: regular satellites may form only where cooling is fast enough to sustain a prograde CPD, a prediction that could be tested with CPD-scale simulations.
  • Because the paper fixes the planet on a circular orbit and uses one mass and viscosity, the natural next step is to let the planet move freely and vary mass, viscosity, and eccentricity; the claim predicts that the torque transition should track the local cooling-to-dynamical timescale ratio across that parameter space.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The manuscript reports 2D global hydrodynamical simulations, using Athena++, of a Jupiter-mass planet accreting from a viscous protoplanetary disk with a β-cooling prescription that relaxes the internal energy toward the initial disk profile. The runs are evolved for 20,000 orbits, and the authors demonstrate that the circumplanetary disk (CPD) accretion reaches a quasi-steady state via mass-flux and angular-momentum budget checks. The paper finds that longer cooling times slightly reduce the planetary accretion rate and change the CPD from a rotationally supported prograde disk (β ≲ 0.1) to a pressure-supported, partially retrograde envelope (β ≳ 10). The central migration claim is a torque-sign transition: the total torque on the planet is positive for efficient cooling and negative for inefficient cooling, with the abstract stating that the transition occurs near β ∼ 1 and attributing it to the disappearance of asymmetric CPD structures that provide a positive torque.

Significance. Concurrent accretion and migration is an important coupling that has only recently been studied self-consistently, and this paper is the first to add a thermodynamic parameter sweep in global 2D simulations. The numerical setup is standard, the runs are long enough to reach a viscous quasi-steady state, and the steady-state interpretation is supported by independent mass-flux and angular-momentum budget checks. If the torque-sign transition is confirmed, it would have direct implications for giant-planet migration and for accreting compact objects in AGN disks. The main weakness is that the load-bearing torque measurements are not covered by the reported convergence tests and the β grid is too coarse to locate the transition robustly; these issues are fixable with additional analysis or simulations.

major comments (3)
  1. [Section 2.3, Fig. 7, and Appendix A] The convergence tests in Appendix A (Fig. A1) validate only the accretion rate ṁ_p; they do not test the gravitational torque whose sign is the paper's central result. The positive torque originates inside ~0.2 r_h (Fig. 9), where the Hill sphere is resolved by only ~20 cells per dimension at the adopted 4-level refinement, so a resolution-dependent change in the inner CPD spiral-arm asymmetry could in principle flip the sign of the integrated torque. Please run the β = 1 convergence cases (5-level refinement, different racc and f, and the high-resolution FARGO3D cases) and report the total gravitational torque, the radial torque profile, and the torque asymmetry Γasy for each; if the torque is not converged, the abstract's β ∼ 1 transition is not established even within the adopted β-cooling model.
  2. [Section 2.3, Fig. 7, and Abstract] The transition 'β ∼ 1' is an interpolation across the widest empty interval in the parameter grid: the runs are at β = 0.01, 0.1, 1, 10, 100, and no run lies between β = 1 and β = 10. The total torque points are shown without any time-variability information, despite the strong short-term fluctuations noted for the high-β runs (Fig. 1 and the running averages used in Fig. 6). Please add intermediate β values (e.g., β = 2, 3, 5) and report time-averaged torques with standard deviations or percentile ranges. Until then, the text should state that the crossing lies between β = 1 and β = 10, not at β ∼ 1.
  3. [Section 2.4, Figs. 8 and 9] The causal mechanism—that the sign change is driven by the disappearance of the asymmetric, rotationally supported CPD—is illustrated only for the two end-member cases (isothermal and β = 100). No quantitative measure of CPD asymmetry as a function of β is provided, so the correlation with the torque sign at intermediate β is not demonstrated. Please add a quantitative asymmetry diagnostic (e.g., Γasy integrated inside the Hill sphere, or the m = 1 Fourier amplitude of the density within ~0.2 r_h) for all runs, or show the torque maps for β = 1 and β = 10.
minor comments (4)
  1. [Section 2.3] In the sentence 'with Γtot > 0 for β ≲ 1 and Γtot < 0 for β1', the second inequality is missing its symbol; it should read 'β ≳ 1'.
  2. [Section 2.1] The text refers to the sound-speed profile as being shown in 'the right panel of Figure 2', but the sound-speed panel is the right panel of Figure 3; the cross-reference should be corrected.
  3. [Section 2.2, Eq. (13)] The quantity C is called a 'constant free parameter', but as an integration constant in Eqs. (9)–(10) it is fixed by the boundary condition at the accretion radius; please reword to avoid implying an additional adjustable parameter.
  4. [Throughout] There are several typographical errors that should be corrected, including 'lunched' for 'launched', 'spacial' for 'spatial', and 'aα−viscosity' for 'an α-viscosity'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the torque-sign transition is a measured simulation outcome, not a fitted or self-referential quantity; the acknowledged β-cooling limitation is a modeling caveat, not a circular reduction.

full rationale

The paper is a numerical parameter study: the central claim that β≲1 produces outward migration and β≳10 inward migration is read off the simulated gravitational and accretional torques (Eqs. 15–16), which are computed from the evolving density field rather than imposed by the cooling prescription. The β-cooling law (Eq. 4) is an input ansatz, explicitly conceded in the Conclusions ('rather than relying on the β-cooling prescription'), so the acknowledged lack of radiative transfer is a validity limitation, not circularity. The isothermal baseline is reproduced in the same code and independently supported by Laune et al. (2024), so the frequent references to the authors' own Li et al. (2024) for setup and torque decomposition are methodological inheritance rather than load-bearing evidence for the new thermodynamic branch. The only notable gaps—Appendix A validates accretion rates but not the torque sign, and no simulation lies between β=1 and β=10—are robustness concerns; they do not make any derived quantity equal to an input by construction. No equation defines torque in terms of β, and no fitted parameter is relabeled as a prediction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard numerical domain assumptions: thin 2D disk, Shakura-Sunyaev viscosity, fixed circular orbit, sink prescription, and beta-cooling relaxation toward the initial profile. These are explicitly stated or acknowledged as limitations. No new physical entities, particles, or forces are introduced.

free parameters (4)
  • Constant C in alpha_con (Eq. 13) = not stated
    Introduced in the angular momentum decomposition for the accretion coefficient alpha_con; the paper says it is a constant free parameter associated with the accretion boundary but does not give its value or fitting procedure.
  • Sink radius racc = 0.1 rh
    Chosen for numerical practicality and tested in Appendix A; not derived from physics.
  • Removal rate f = 5 Omega
    Sink prescription parameter following Li et al. (2024); convergence tested in Appendix A.
  • Potential softening s = 0.1 rh
    Gravitational softening length chosen and tested in Appendix A.
assumptions (5)
  • domain assumption beta-cooling relaxation (Eq. 4) represents disk thermodynamics
    The entire parameter study varies beta while relaxing internal energy toward the initial profile; the authors acknowledge radiative hydrodynamics may change the CPD structure and torque.
  • domain assumption 2D thin-disk approximation (h = 0.05) is adequate
    Simulations are 2D; the authors state that the extent of 3D effects with beta-cooling remains unclear.
  • domain assumption Shakura-Sunyaev alpha viscosity with alpha = 0.01
    The disk is laminar and viscous; magnetic turbulence may modify spiral waves and torques, as conceded in the Conclusions.
  • domain assumption Fixed circular orbit with post-processed torques
    The planet is held on a circular orbit and migration is inferred from torques; accreted mass and angular momentum are not added back to the planet.
  • domain assumption Non-self-gravitating disk
    Disk self-gravity is neglected; the paper does not assess its effect on the reported torques.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Effects of Thermodynamics on the Concurrent Accretion and Migration of Gas Giants in Protoplanetary Disks." pith.science (2026). https://pith.science/paper/7JDYS3AH

@misc{pith2026250115874,
  author       = {Pith},
  title        = {Pith review of: Effects of Thermodynamics on the Concurrent Accretion and Migration of Gas Giants in Protoplanetary Disks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7JDYS3AH}},
  note         = {Machine review of arXiv:2501.15874}
}
abstract

Accretion and migration usually proceeds concurrently for giant planet formation in the natal protoplanetary disks. Recent works indicate that the concurrent accretion onto a giant planet imposes significant impact on the planetary migration dynamics in the isothermal regime. In this work, we carry out a series of 2D global hydrodynamical simulations with Athena++ to explore the effect of thermodynamics on the concurrent accretion and migration process of the planets in a self-consistent manner. The thermodynamics effect is modeled with a thermal relaxation timescale using a $\beta$-cooling prescription. Our results indicate that radiative cooling has a substantial effect on the accretion and migration processes of the planet. As cooling timescales increase, we observe a slight decrease in the planetary accretion rate, and a transition from the outward migrating into inward migration. This transition occurs approximately when the cooling timescale is comparable to the local dynamical timescale ($\beta\sim1$), which is closely linked to the asymmetric structures from the circumplanetary disk (CPD) region. The asymmetric structures in the CPD region which appear with an efficient cooling provide a strong positive torque driving the planet migrate outward. However, such a positive torque is strongly suppressed, when the CPD structures tend to disappear with a relatively long cooling timescale ($\beta\gtrsim10$). Our findings may also be relevant to the dynamical evolution of accreting stellar-mass objects embedded in disks around active galactic nuclei.

Figures

Figures reproduced from arXiv: 2501.15874 by the authors.

Figure 1
Figure 1. The left panel displays the running time-averaged planetary accretion rates in a locally isothermal disk and disks with varying β-cooling timescales, measured in unit of Σ0r 2 0Ω0. The black dashed line indicates the material supply rate from the outer boundary. The right panel illustrates the short-term fluctuations in accretion rates for several representative simulations, without any time averaging [PITH_FULL_IM… view at source ↗
Figure 2
Figure 2. The density distribution δΣ in the vicinity of the planet with different cooling timescales. δΣ = Σ − ⟨Σ⟩ where ⟨Σ⟩ is the azimuthally averaged surface density from the perturbed disk at the same orbital time. The arrows in the plots represent the velocity vectors relative to the planet. All plots are presented at 20000 orbits. For the cases with β = 10 and β = 100, time averages over 100 and 500 orbits, respectivel… view at source ↗
Figure 3
Figure 3. Left panel: the azimuthally-averaged rotation velocity relative to the planet for different models in unit of the local Keplerian velocity orbiting around the star. The black line represents the Keplerian rotation velocity around the planet. Middle panel: the surface density profile around the planet in unit of Σ0. Right panel: the azimuthally-averaged sound speed cs in the vicinity of the planet in code unit. To fa… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Different accretion coefficient calculated by Equation 10 under isothermal EOS (left panel) and β = 100 (right panel) cases. The the summation of αrey, αcon and αT is shown as red lines [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Left panel: the effective accretion coefficients in Equation 11 under different cooling timescales. Right panel: the accretion coefficients resulting from Reynolds stress(αrey; solid lines) and external forces (αT; dashed lines) for different cooling timescales. The sa…
Figure 6
Figure 6. Figure 6: The semi-major axis evolution due to the gravitational (blue lines), accretional (red lines) and total (black lines) torques in isothermal (left panel) and β = 100 (right panel) cases. For the case of β = 100, a running-time averaged over 500 orbits is carried out to s…
Figure 7
Figure 7. Figure 7: The torque exerted on the planet under different cooling timescales in code unit, where ℓ0 = r 2 0Ω0 is the specific angular momentum of the disk at r0. The blue and red circle points represent the gravitational torque and accretional torque respectively. The black squ…
Figure 8
Figure 8. Figure 8: Spacial distribution of gravitational torques in the vicinity of the planet around 20000 orbits. The upper panel represents the isothermal condition and the lower panel shows the β = 100 case. A time-averaging over 500 orbits is done for the β = 100 case. The contour i…
Figure 9
Figure 9. Figure 9: The cumulative radial distribution (integration from rin to r) of the gravitational torque exerted onto the planet, where the blue (red) line represents the isothermal (β = 100) case. The torque for β = 100 is time-averaged over 500 orbits around 20000 orbits. The two …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

68 extracted references · 36 canonical work pages

  1. [1]

    Characteristics of Planetary Candidates Observed by Kepler

    Borucki, W.J.; Koch, D.G.; Basri, G.; Batalha, N.; Brown, T.M.; Bryson, S.T.; Caldwell, D.; Christensen-Dalsgaard, J.; Cochran, W.D.; DeVore, E.; et al. Characteristics of Planetary Candidates Observed by Kepler. II. Analysis of the First Four Months of Data. Astrophys. J. 2011, 736, 19, [arXiv:astro-ph.EP/1102.0541]. https://doi.org/10.1088/0004-637X/736/1/19

    arXiv 2011

  2. [2]

    A Jupiter-mass companion to a solar-type star

    Mayor, M.; Queloz, D. A Jupiter-mass companion to a solar-type star. Nature 1995, 378, 355–359. https://doi.org/10.1038/3783 55a0

    work page doi:10.1038/3783 1995

  3. [3]

    On the Tidal Interaction between Protoplanets and the Protoplanetary Disk

    Lin, D.N.C.; Papaloizou, J. On the Tidal Interaction between Protoplanets and the Protoplanetary Disk. III. Orbital Migration of Protoplanets. Astrophys. J. 1986, 309, 846. https://doi.org/10.1086/164653

    doi:10.1086/164653 1986

  4. [4]

    Planet Migration in Planetesimal Disks

    Levison, H.F.; Morbidelli, A.; Gomes, R.; Backman, D. Planet Migration in Planetesimal Disks. In Proceedings of the Protostars and Planets V; Reipurth, B.; Jewitt, D.; Keil, K., Eds., jan 2007, p. 669

    work page 2007

  5. [5]

    A record of the final phase of giant planet migration fossilized in the asteroid belt's orbital structure

    Clement, M.S.; Morbidelli, A.; Raymond, S.N.; Kaib, N.A. A record of the final phase of giant planet migration fossilized in the asteroid belt’s orbital structure. Mon. Not. R. Astron. Soc. 2020, 492, L56–L60, [arXiv:astro-ph.EP/1912.02833]. https: //doi.org/10.1093/mnrasl/slz184

    work page Pith review arXiv 2020

  6. [6]

    A Closely-Packed System of Low-Mass, Low-Density Planets Transiting Kepler-11

    Lissauer, J.J.; Fabrycky, D.C.; Ford, E.B.; Borucki, W.J.; Fressin, F.; Marcy, G.W.; Orosz, J.A.; Rowe, J.F.; Torres, G.; Welsh, W.F.; et al. A closely packed system of low-mass, low-density planets transiting Kepler-11. Nature 2011, 470, 53–58, [arXiv:astro- ph.EP/1102.0291]. https://doi.org/10.1038/nature09760

    work page Pith review arXiv 2011

  7. [7]

    Overstable Librations can Account for the Paucity of Mean Motion Resonances among Exoplanet Pairs

    Goldreich, P .; Schlichting, H.E. Overstable Librations can Account for the Paucity of Mean Motion Resonances among Exoplanet Pairs. Astron. J. 2014, 147, 32, [arXiv:astro-ph.EP/1308.4688]. https://doi.org/10.1088/0004-6256/147/2/32

    arXiv 2014

  8. [8]

    Migration of Planets Into and Out of Mean Motion Resonances in Protoplanetary Discs: Overstability of Capture and Nonlinear Eccentricity Damping

    Xu, W.; Lai, D.; Morbidelli, A. Migration of planets into and out of mean motion resonances in protoplanetary discs: overstability of capture and non-linear eccentricity damping. Mon. Not. R. Astron. Soc. 2018, 481, 1538–1549, [arXiv:astro-ph.EP/1805.07501]. https://doi.org/10.1093/mnras/sty2406

    work page Pith review arXiv 2018

Show all 68 references
  1. [9]

    Mean-motion resonances with interfering density waves

    Yang, H.; Li, Y.P . Mean-motion resonances with interfering density waves. Mon. Not. R. Astron. Soc. 2024, 534, 485–501, [arXiv:astro-ph.EP/2309.15694]. https://doi.org/10.1093/mnras/stae2097

    2024 arXiv

  2. [10]

    Comet 81P/Wild 2 Under a Microscope

    Brownlee, D.; Tsou, P .; Aléon, J.; Alexander, C.M.O.D.; Araki, T.; Bajt, S.; Baratta, G.A.; Bastien, R.; Bland, P .; Bleuet, P .; et al. Comet 81P/Wild 2 Under a Microscope. Science 2006, 314, 1711. https://doi.org/10.1126/science.1135840

    2006 doi

  3. [11]

    Review of Jupiter-Trojan asteroids research

    Huang, H.; Wu, Y. Review of Jupiter-Trojan asteroids research. Reviews of Geophysics and Planetary Physics 2024, 55, 175–183. https://doi.org/10.19975/j.dqyxx.2023-022

    2024 doi

  4. [12]

    Protoplanet Migration by Nebula Tides

    Ward, W.R. Protoplanet Migration by Nebula Tides. Icarus 1997, 126, 261–281. https://doi.org/10.1006/icar.1996.5647

    1997

  5. [13]

    Disk-satellite interactions

    Goldreich, P .; Tremaine, S. Disk-satellite interactions. Astrophys. J. 1980, 241, 425–441. https://doi.org/10.1086/158356

    1980 doi

  6. [14]

    On the Wave Excitation and a Generalized Torque Formula for Lindblad Resonances Excited by External Potential

    Artymowicz, P . On the Wave Excitation and a Generalized Torque Formula for Lindblad Resonances Excited by External Potential. Astrophys. J. 1993, 419, 155. https://doi.org/10.1086/173469

    1993 doi

  7. [15]

    Horsehoe Orbit Drag

    Ward, W.R. Horsehoe Orbit Drag. In Proceedings of the Lunar and Planetary Science Conference, mar 1991, Vol. 22, Lunar and Planetary Science Conference, p. 1463

    1991

  8. [16]

    On the Co-orbital Corotation Torque in a Viscous Disk and Its Impact on Planetary Migration

    Masset, F.S. On the Co-orbital Corotation Torque in a Viscous Disk and Its Impact on Planetary Migration. Astrophys. J. 2001, 558, 453–462, [arXiv:astro-ph/astro-ph/0205209]. https://doi.org/10.1086/322446

    2001 arXiv

  9. [17]

    On the tidal interaction between protoplanets and the primordial solar nebula

    Papaloizou, J.; Lin, D.N.C. On the tidal interaction between protoplanets and the primordial solar nebula. I - Linear calculation of the role of angular momentum exchange. Astrophys. J. 1984, 285, 818–834. https://doi.org/10.1086/162561

    1984 doi

  10. [18]

    Three-Dimensional Interaction between a Planet and an Isothermal Gaseous Disk

    Tanaka, H.; Takeuchi, T.; Ward, W.R. Three-Dimensional Interaction between a Planet and an Isothermal Gaseous Disk. I. Corotation and Lindblad Torques and Planet Migration. Astrophys. J. 2002, 565, 1257–1274. https://doi.org/10.1086/324713

    2002 doi

  11. [19]

    Planet-Disk Interaction and Orbital Evolution

    Kley, W.; Nelson, R.P . Planet-Disk Interaction and Orbital Evolution. Ann. Rev. Astron. Astrophys. 2012, 50, 211–249, [arXiv:astro-ph.EP/1203.1184]. https://doi.org/10.1146/annurev-astro-081811-125523

    2012 arXiv

  12. [20]

    Planet-Disk Interactions and Orbital Evolution

    Paardekooper, S.; Dong, R.; Duffell, P .; Fung, J.; Masset, F.S.; Ogilvie, G.; Tanaka, H. Planet-Disk Interactions and Orbital Evolution. In Proceedings of the Protostars and Planets VII; Inutsuka, S.; Aikawa, Y.; Muto, T.; Tomida, K.; Tamura, M., Eds., jul 2023, Vol. 534, Ast...

    2023 doi arXiv

  13. [21]

    On the Tidal Interaction between Protoplanets and the Primordial Solar Nebula

    Lin, D.N.C.; Papaloizou, J. On the Tidal Interaction between Protoplanets and the Primordial Solar Nebula. II. Self-Consistent Nonlinear Interaction. Astrophys. J. 1986, 307, 395. https://doi.org/10.1086/164426

    1986 doi

  14. [22]

    Calculations of the accretion and evolution of giant planets: The effects of solid cores

    Bodenheimer, P .; Pollack, J.B. Calculations of the accretion and evolution of giant planets: The effects of solid cores. Icarus 1986, 67, 391–408. https://doi.org/10.1016/0019-1035(86)90122-3. Universe 2025, 1, 0 16 of 17

    1986 doi

  15. [23]

    Formation of the Giant Planets by Concurrent Accretion of Solids and Gas

    Pollack, J.B.; Hubickyj, O.; Bodenheimer, P .; Lissauer, J.J.; Podolak, M.; Greenzweig, Y. Formation of the Giant Planets by Concurrent Accretion of Solids and Gas. Icarus 1996, 124, 62–85. https://doi.org/10.1006/icar.1996.0190

    1996

  16. [24]

    Toward a Deterministic Model of Planetary Formation

    Ida, S.; Lin, D.N.C. Toward a Deterministic Model of Planetary Formation. I. A Desert in the Mass and Semimajor Axis Distributions of Extrasolar Planets. Astrophys. J. 2004, 604, 388–413, [arXiv:astro-ph/astro-ph/0312144]. https://doi.org/10.1086/ 381724

    2004 arXiv

  17. [25]

    The Preservation of Super-Earths and the Emergence of Gas Giants after Their Progenitor Cores Have Entered the Pebble-isolation Phase

    Chen, Y.X.; Li, Y.P .; Li, H.; Lin, D.N.C. The Preservation of Super-Earths and the Emergence of Gas Giants after Their Progenitor Cores Have Entered the Pebble-isolation Phase. Astrophys. J. 2020, 896, 135, [arXiv:astro-ph.EP/2005.10974]. https://doi.org/10.3 847/1538-4357/ab9604

    2020 arXiv

  18. [26]

    Angular Momentum Accretion onto a Gas Giant Planet

    Machida, M.N.; Kokubo, E.; Inutsuka, S.i.; Matsumoto, T. Angular Momentum Accretion onto a Gas Giant Planet. Astrophys. J. 2008, 685, 1220–1236, [arXiv:astro-ph/0801.3305]. https://doi.org/10.1086/590421

    2008 arXiv

  19. [27]

    Distribution of Accreting Gas and Angular Momentum onto Circumplanetary Disks

    Tanigawa, T.; Ohtsuki, K.; Machida, M.N. Distribution of Accreting Gas and Angular Momentum onto Circumplanetary Disks. Astrophys. J. 2012, 747, 47, [arXiv:astro-ph.EP/1112.3706]. https://doi.org/10.1088/0004-637X/747/1/47

    2012 arXiv

  20. [28]

    Circumplanetary Disk Dynamics in the Isothermal and Adiabatic Limits

    Fung, J.; Zhu, Z.; Chiang, E. Circumplanetary Disk Dynamics in the Isothermal and Adiabatic Limits. Astrophys. J. 2019, 887, 152, [arXiv:astro-ph.EP/1909.09655]. https://doi.org/10.3847/1538-4357/ab53da

    2019 arXiv

  21. [29]

    3D global simulations of accretion onto gap-opening planets: implications for circumplanetary disc structures and accretion rates

    Li, Y.P .; Chen, Y.X.; Lin, D.N.C. 3D global simulations of accretion onto gap-opening planets: implications for circumplanetary disc structures and accretion rates. Mon. Not. R. Astron. Soc. 2023, 526, 5346–5364, [arXiv:astro-ph.EP/2310.02822]. https: //doi.org/10.1093/mnras/stad3049

    2023 arXiv

  22. [30]

    Three-dimensional Simulations of a Planet Embedded in a Protoplanetary Disk

    Kley, W.; D’Angelo, G.; Henning, T. Three-dimensional Simulations of a Planet Embedded in a Protoplanetary Disk. Astrophys. J. 2001, 547, 457–464. https://doi.org/10.1086/318345

    2001 doi

  23. [31]

    Orbital Migration and Mass Accretion of Protoplanets in Three-dimensional Global Computations with Nested Grids

    D’Angelo, G.; Kley, W.; Henning, T. Orbital Migration and Mass Accretion of Protoplanets in Three-dimensional Global Computations with Nested Grids. Astrophys. J. 2003, 586, 540–561, [arXiv:astro-ph/astro-ph/0308055]. https://doi.org/10.1086/ 367555

    2003 arXiv

  24. [32]

    Gas accretion onto a protoplanet and formation of a gas giant planet

    Machida, M.N.; Kokubo, E.; Inutsuka, S.I.; Matsumoto, T. Gas accretion onto a protoplanet and formation of a gas giant planet. Mon. Not. R. Astron. Soc. 2010, 405, 1227–1243, [arXiv:astro-ph.SR/1002.3002]. https://doi.org/10.1111/j.1365-2966.2010.16527.x

    2010 arXiv

  25. [33]

    Deuterium Burning in Massive Giant Planets and Low-mass Brown Dwarfs Formed by Core-nucleated Accretion

    Bodenheimer, P .; D’Angelo, G.; Lissauer, J.J.; Fortney, J.J.; Saumon, D. Deuterium Burning in Massive Giant Planets and Low-mass Brown Dwarfs Formed by Core-nucleated Accretion. Astrophys. J. 2013, 770, 120, [arXiv:astro-ph.EP/1305.0980]. https://doi.org/10.1088/0004-637X/770/2/120

    2013 arXiv

  26. [34]

    The maximum accretion rate of a protoplanet: how fast can runaway be? Mon

    Choksi, N.; Chiang, E.; Fung, J.; Zhu, Z. The maximum accretion rate of a protoplanet: how fast can runaway be? Mon. Not. R. Astron. Soc. 2023, 525, 2806–2819, [arXiv:astro-ph.EP/2305.01684]. https://doi.org/10.1093/mnras/stad2269

    2023 arXiv

  27. [35]

    Accretion of Gas Giants Constrained by the Tidal Barrier.Astrophys

    Li, Y.P .; Chen, Y.X.; Lin, D.N.C.; Zhang, X. Accretion of Gas Giants Constrained by the Tidal Barrier.Astrophys. J. 2021, 906, 52, [arXiv:astro-ph.EP/2011.02869]. https://doi.org/10.3847/1538-4357/abc883

    2021 arXiv

  28. [36]

    Tidal Barrier and the Asymptotic Mass of Proto-Gas Giant Planets

    Dobbs-Dixon, I.; Li, S.L.; Lin, D.N.C. Tidal Barrier and the Asymptotic Mass of Proto-Gas Giant Planets. Astrophys. J. 2007, 660, 791–806, [arXiv:astro-ph/astro-ph/0701269]. https://doi.org/10.1086/512537

    2007 arXiv

  29. [37]

    The Migration of Gap-opening Planets is Not Locked to Viscous Disk Evolution

    Duffell, P .C.; Haiman, Z.; MacFadyen, A.I.; D’Orazio, D.J.; Farris, B.D. The Migration of Gap-opening Planets is Not Locked to Viscous Disk Evolution. Astrophys. J. Lett. 2014, 792, L10, [arXiv:astro-ph.EP/1405.3711]. https://doi.org/10.1088/2041-8205/79 2/1/L10

    2014 arXiv

  30. [38]

    How Empty are Disk Gaps Opened by Giant Planets? Astrophys

    Fung, J.; Shi, J.M.; Chiang, E. How Empty are Disk Gaps Opened by Giant Planets? Astrophys. J. 2014, 782, 88, [arXiv:astro- ph.EP/1310.0156]. https://doi.org/10.1088/0004-637X/782/2/88

    2014 arXiv

  31. [39]

    Migration of massive planets in accreting disks

    Dürmann, C.; Kley, W. Migration of massive planets in accreting disks. Astron. Astrophys. 2015, 574, A52, [arXiv:astro- ph.EP/1411.3190]. https://doi.org/10.1051/0004-6361/201424837

    2015 arXiv

  32. [40]

    Toward a new paradigm for Type II migration

    Robert, C.M.T.; Crida, A.; Lega, E.; Méheut, H.; Morbidelli, A. Toward a new paradigm for Type II migration. Astron. Astrophys. 2018, 617, A98, [arXiv:astro-ph.EP/1808.00381]. https://doi.org/10.1051/0004-6361/201833539

    2018 arXiv

  33. [41]

    Retention of Long-period Gas Giant Planets: Type II Migration Revisited

    Chen, Y.X.; Zhang, X.; Li, Y.P .; Li, H.; Lin, D.N.C. Retention of Long-period Gas Giant Planets: Type II Migration Revisited. Astrophys. J. 2020, 900, 44, [arXiv:astro-ph.EP/2007.14905]. https://doi.org/10.3847/1538-4357/abaab6

    2020 arXiv

  34. [42]

    Radial Migration of Gap-opening Planets in Protoplanetary Disks

    Kanagawa, K.D.; Tanaka, H.; Szuszkiewicz, E. Radial Migration of Gap-opening Planets in Protoplanetary Disks. I. The Case of a Single Planet. Astrophys. J. 2018, 861, 140, [arXiv:astro-ph.EP/1805.11101]. https://doi.org/10.3847/1538-4357/aac8d9

    2018 arXiv

  35. [43]

    Shock-driven Accretion in Circumplanetary Disks: Observables and Satellite Formation

    Zhu, Z.; Ju, W.; Stone, J.M. Shock-driven Accretion in Circumplanetary Disks: Observables and Satellite Formation. Astrophys. J. 2016, 832, 193, [arXiv:astro-ph.EP/1609.09250]. https://doi.org/10.3847/0004-637X/832/2/193

    2016 arXiv

  36. [44]

    Circumplanetary disc or circumplanetary envelope? Mon

    Szulágyi, J.; Masset, F.; Lega, E.; Crida, A.; Morbidelli, A.; Guillot, T. Circumplanetary disc or circumplanetary envelope? Mon. Not. R. Astron. Soc. 2016, 460, 2853–2861, [arXiv:astro-ph.EP/1605.04586]. https://doi.org/10.1093/mnras/stw1160

    2016 arXiv

  37. [45]

    A Thermodynamic Criterion for the Formation of Circumplanetary Disks

    Krapp, L.; Kratter, K.M.; Youdin, A.N.; Benítez-Llambay, P .; Masset, F.; Armitage, P .J. A Thermodynamic Criterion for the Formation of Circumplanetary Disks. Astrophys. J. 2024, 973, 153, [arXiv:astro-ph.EP/2402.14638]. https://doi.org/10.3847/1538 -4357/ad644a

    2024 arXiv

  38. [46]

    Hot Circumsingle Disks Drive Binary Black Hole Mergers in Active Galactic Nucleus Disks

    Li, Y.P .; Dempsey, A.M.; Li, H.; Li, S.; Li, J. Hot Circumsingle Disks Drive Binary Black Hole Mergers in Active Galactic Nucleus Disks. Astrophys. J. Lett. 2022, 928, L19, [arXiv:astro-ph.HE/2112.11057]. https://doi.org/10.3847/2041-8213/ac60fd

    2022 arXiv

  39. [47]

    How cooling influences circumbinary discs.Astron

    Sudarshan, P .; Penzlin, A.B.T.; Ziampras, A.; Kley, W.; Nelson, R.P . How cooling influences circumbinary discs.Astron. Astrophys. 2022, 664, A157, [arXiv:astro-ph.EP/2206.07749]. https://doi.org/10.1051/0004-6361/202243472

    2022 arXiv

  40. [48]

    On the Role of Dynamical Cooling in the Dynamics of Circumbinary Disks

    Wang, H.Y.; Bai, X.N.; Lai, D. On the Role of Dynamical Cooling in the Dynamics of Circumbinary Disks. Astrophys. J. 2023, 943, 175, [arXiv:astro-ph.HE/2212.04199]. https://doi.org/10.3847/1538-4357/acac77. Universe 2025, 1, 0 17 of 17

    2023 arXiv

  41. [49]

    Planet-Disk Interaction in Disks with Cooling: Basic Theory

    Miranda, R.; Rafikov, R.R. Planet-Disk Interaction in Disks with Cooling: Basic Theory. Astrophys. J. 2020, 892, 65, [arXiv:astro- ph.EP/1911.01428]. https://doi.org/10.3847/1538-4357/ab791a

    2020 arXiv

  42. [50]

    The effects of disc self-gravity and radiative cooling on the formation of gaps and spirals by young planets

    Zhang, S.; Zhu, Z. The effects of disc self-gravity and radiative cooling on the formation of gaps and spirals by young planets. Mon. Not. R. Astron. Soc. 2020, 493, 2287–2305, [arXiv:astro-ph.EP/1911.01530]. https://doi.org/10.1093/mnras/staa404

    2020 arXiv

  43. [51]

    Modelling planet-induced gaps and rings in ALMA discs: the role of in-plane radiative diffusion

    Ziampras, A.; Nelson, R.P .; Rafikov, R.R. Modelling planet-induced gaps and rings in ALMA discs: the role of in-plane radiative diffusion. Mon. Not. R. Astron. Soc. 2023, 524, 3930–3947, [arXiv:astro-ph.EP/2305.14415]. https://doi.org/10.1093/mnras/stad1 973

    2023 arXiv

  44. [52]

    The Dependence of the Structure of Planet-opened Gaps in Protoplanetary Disks on Radiative Cooling

    Zhang, M.; Huang, P .; Dong, R. The Dependence of the Structure of Planet-opened Gaps in Protoplanetary Disks on Radiative Cooling. Astrophys. J. 2024, 961, 86, [arXiv:astro-ph.EP/2310.11757]. https://doi.org/10.3847/1538-4357/ad055c

    2024 arXiv

  45. [53]

    On the Horseshoe Drag of a Low-Mass Planet

    Masset, F.S.; Casoli, J. On the Horseshoe Drag of a Low-Mass Planet. II. Migration in Adiabatic Disks. Astrophys. J. 2009, 703, 857–876, [arXiv:astro-ph.EP/0907.4676]. https://doi.org/10.1088/0004-637X/703/1/857

    2009 arXiv

  46. [54]

    A torque formula for non-isothermal type I planetary migration - I

    Paardekooper, S.J.; Baruteau, C.; Crida, A.; Kley, W. A torque formula for non-isothermal type I planetary migration - I. Unsaturated horseshoe drag. Mon. Not. R. Astron. Soc. 2010, 401, 1950–1964, [arXiv:astro-ph.EP/0909.4552]. https://doi.org/10.1 111/j.1365-2966.2009.15782.x

    2010 arXiv

  47. [55]

    Migration of Earth-sized planets in 3D radiative discs

    Lega, E.; Crida, A.; Bitsch, B.; Morbidelli, A. Migration of Earth-sized planets in 3D radiative discs. Mon. Not. R. Astron. Soc. 2014, 440, 683–695, [arXiv:astro-ph.EP/1402.2834]. https://doi.org/10.1093/mnras/stu304

    2014 arXiv

  48. [56]

    Concurrent Accretion and Migration of Giant Planets in Their Natal Disks with Consistent Accretion Torque

    Li, Y.P .; Chen, Y.X.; Lin, D.N.C. Concurrent Accretion and Migration of Giant Planets in Their Natal Disks with Consistent Accretion Torque. Astrophys. J. 2024, 971, 130, [arXiv:astro-ph.EP/2406.12716]. https://doi.org/10.3847/1538-4357/ad5a06

    2024 arXiv

  49. [57]

    Migration of Accreting Planets and Black Holes in Disks

    Laune, J.; Li, R.; Lai, D. Migration of Accreting Planets and Black Holes in Disks. arXiv e-prints 2024, p. arXiv:2405.00296, [arXiv:astro-ph.EP/2405.00296]. https://doi.org/10.48550/arXiv.2405.00296

    2024 doi arXiv

  50. [58]

    The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohy- drodynamic Solvers

    Stone, J.M.; Tomida, K.; White, C.J.; Felker, K.G. The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohy- drodynamic Solvers. Astrophys. J. Suppl. Ser. 2020, 249, 4, [arXiv:astro-ph.IM/2005.06651]. https://doi.org/10.3847/1538-4365/ ab929b

    2020 arXiv

  51. [59]

    Observations of Protoplanetary Disk Structures

    Andrews, S.M. Observations of Protoplanetary Disk Structures. Ann. Rev. Astron. Astrophys. 2020, 58, 483–528, [arXiv:astro- ph.EP/2001.05007]. https://doi.org/10.1146/annurev-astro-031220-010302

    2020 arXiv

  52. [60]

    Setting the Stage for Planet Formation: Measurements and Implications of the Fundamental Disk Properties

    Miotello, A.; Kamp, I.; Birnstiel, T.; Cleeves, L.C.; Kataoka, A. Setting the Stage for Planet Formation: Measurements and Implications of the Fundamental Disk Properties. In Proceedings of the Protostars and Planets VII; Inutsuka, S.; Aikawa, Y.; Muto, T.; Tomida, K.; Tamura,...

    2023 doi arXiv

  53. [61]

    Black holes in binary systems

    Shakura, N.I.; Sunyaev, R.A. Black holes in binary systems. Observational appearance. Astron. Astrophys. 1973, 24, 337–355

    1973

  54. [62]

    The Structure of Spiral Shocks Excited by Planetary-mass Companions

    Zhu, Z.; Dong, R.; Stone, J.M.; Rafikov, R.R. The Structure of Spiral Shocks Excited by Planetary-mass Companions. Astrophys. J. 2015, 813, 88, [arXiv:astro-ph.SR/1507.03599]. https://doi.org/10.1088/0004-637X/813/2/88

    2015 arXiv

  55. [63]

    A comparative study of disc-planet interaction

    de Val-Borro, M.; Edgar, R.G.; Artymowicz, P .; Ciecielag, P .; Cresswell, P .; D’Angelo, G.; Delgado-Donate, E.J.; Dirksen, G.; Fromang, S.; Gawryszczak, A.; et al. A comparative study of disc-planet interaction. Mon. Not. R. Astron. Soc. 2006, 370, 529–558, [arXiv:astro-ph/a...

    2006 arXiv

  56. [64]

    Orbital Evolution of Binary Black Holes in Active Galactic Nucleus Disks: A Disk Channel for Binary Black Hole Mergers? Astrophys

    Li, Y.P .; Dempsey, A.M.; Li, S.; Li, H.; Li, J. Orbital Evolution of Binary Black Holes in Active Galactic Nucleus Disks: A Disk Channel for Binary Black Hole Mergers? Astrophys. J. 2021, 911, 124, [arXiv:astro-ph.HE/2101.09406]. https://doi.org/10.3847/ 1538-4357/abed48

    2021 arXiv

  57. [65]

    Hydrodynamical evolution of black-hole binaries embedded in AGN discs

    Li, R.; Lai, D. Hydrodynamical evolution of black-hole binaries embedded in AGN discs. Mon. Not. R. Astron. Soc. 2022, 517, 1602–1624, [arXiv:astro-ph.HE/2202.07633]. https://doi.org/10.1093/mnras/stac2577

    2022 arXiv

  58. [66]

    Evolution of the Solar Activity over Time and Effects on Planetary Atmospheres

    Ribas, I.; Guinan, E.F.; Güdel, M.; Audard, M. Evolution of the Solar Activity over Time and Effects on Planetary Atmospheres. I. High-Energy Irradiances (1-1700 Å). Astrophys. J. 2005, 622, 680–694, [arXiv:astro-ph/astro-ph/0412253]. https://doi.org/10.108 6/427977

    2005 arXiv

  59. [67]

    The role of massive AGB stars in the early solar system composition

    Trigo-Rodríguez, J.M.; García-Hernández, D.A.; Lugaro, M.; Karakas, A.I.; van Raai, M.; García Lario, P .; Manchado, A. The role of massive AGB stars in the early solar system composition. M&PS 2009, 44, 627–641, [arXiv:astro-ph/0812.4358]. https://doi.org/10.1111/j.1945-5100....

    2009 arXiv

  60. [68]

    FARGO3D: A New GPU-oriented MHD Code

    Benítez-Llambay, P .; Masset, F.S. FARGO3D: A New GPU-oriented MHD Code. Astrophys. J. Suppl. Ser. 2016, 223, 11, [arXiv:astro-ph.IM/1602.02359]. https://doi.org/10.3847/0067-0049/223/1/11. Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publica...

    2016 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.