PDS 70 c and SR 12 c: Observational Constraints on Giant-Planet and Satellite Formation

Ignacio Mosqueira

REVIEW 2 major objections 4 minor 105 references

PDS 70 c and SR 12 c: Observational Constraints on Giant-Planet and Satellite Formation

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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

Pith's one-line read The compact millimeter source at PDS 70 c is a moon-forming circumplanetary disk whose dust mass brackets Callisto's, and the system's age falls inside the window where such disks should still be building regular satellites.

desk verdict Worth a serious refereeing: clean observational synthesis and honest bookkeeping, but the 'strong support' chronometric claim leans on self-cited model timescales that are never re-derived or shown to transfer to PDS 70 c. read the letter →

arxiv 2608.10409 v1 pith:MKQZLMX5 submitted 2026-08-11 astro-ph.EP astro-ph.SR

Ignacio Mosqueira This is my paper · ORCID

classification astro-ph.EPastro-ph.SR

keywords circumplanetarydiskssatelliteformationPDS70SR12cprotoplanetaryplanetary-masscompanionssubmillimetercontinuumregularsatellites

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 argues that the only two secure cold submillimeter detections of disks around bound planetary-mass objects—PDS 70 c and SR 12 c—are snapshots of moon formation, not leftover debris. The 855-micron flux at PDS 70 c corresponds to 0.007–0.031 Earth masses of dust, comparable to Callisto, and the emitting region's 0.6–1.2 au scale matches the circularization radius expected for gas falling in through a mature planetary gap. SR 12 c, whose planet has essentially stopped growing, still holds gas and dust, showing that a moon-forming reservoir can outlive planetary growth. The paper's chronological kicker is that PDS 70's age, 5.4 ± 1.0 million years, falls between the model's Callisto (about 1 million years) and Iapetus (about 10 million years) formation timescales, placing the system in an active satellite-building window. If correct, this connects giant-planet gap opening to the timing and architecture of regular-satellite systems like Jupiter's.

What carries the argument

The argument is carried by three linked objects. The circumplanetary disk, the rotationally supported reservoir within a planet's Hill sphere, is the site where moons assemble; the paper reads the PDS 70 c continuum as a direct image of such a reservoir. The central geometric identity is $r_c = (\lambda^2/3) R_H$, where $R_H$ is the Hill radius and $\lambda$ is the dimensionless specific angular momentum of gas entering the Hill sphere: pre-gap inflow gives $\lambda = 1/4$ and $r_c = R_H/48$, while gap-fed inflow through the $L_1$ and $L_2$ regions gives $\lambda \approx 0.87$ and $r_c \approx R_H/3$, matching the observed 0.6–1.2 au scale. The third element is the solids-enhanced minimum-mass model, which sets moon formation timescales by gas-drag clearing of satellitesimals rather than by local accretion rates, yielding about $10^6$ yr for Callisto and about $10^7$ yr for Iapetus; these timescales bracket the PDS 70 age and turn the continuum detections into a chronological test.

What would settle it

Recompute the Callisto and Iapetus gas-drag clearing timescales using PDS 70-like disk parameters and independently re-measure the PDS 70 system age; if the resulting formation window does not contain 5.4 ± 1.0 Myr, or if a high-resolution continuum measurement places the PDS 70 c emitting radius outside roughly 0.6–1.2 au, the paper's central chronological and radial-scale claims are falsified.

Watch

Extended reading notes

Core claim

The central discovery claim is that the compact 855-µm continuum source associated with PDS 70 c is a circumplanetary disk in the process of forming regular satellites, and that SR 12 c provides an independent second example of a planetary-mass disk that retains both gas and solids after its host has finished growing. In the optically thin limit the radiating dust mass is 0.007–0.031 $M_\oplus$ at 26 K, bracketing Callisto's 0.018 $M_\oplus$; in the optically thick limit the same flux demands a minimum coplanar emitting radius of 0.58–0.66 au, close to the ALMA upper limit of about 1.2 au and to the predicted late gap-fed circularization radius $r_c \sim R_H/3$. The author further claims that both planets accreting inside one common circumstellar gap make the gap a finite reservoir: planetary torques deplete it on timescales of a few thousand years, shutting off circumplanetary supply and linking final planet masses to disk properties. Because gas-drag clearing of satellitesimals in the author's solids-enhanced minimum-mass model gives Callisto about $10^6$ yr and Iapetus about $10^7$ yr formation timescales, the measured PDS 70 age of 5.4 ± 1.0 Myr sits inside the active satellite-formation window, supporting a quiescent, solids-enhanced moon-forming environment.

Load-bearing premise

The argument's load-bearing premise is that the gas-drag clearing timescales computed in the author's earlier model—about $10^{6}$ years for Callisto and $10^{7}$ years for Iapetus—are correct and transfer to the PDS 70 environment; if those timescales are wrong by an order of magnitude, PDS 70's 5.4-million-year age no longer sits between them, and the chronological support collapses.

Editorial extensions

If this is right

If PDS 70 c is actively forming moons, the system's 5.4-million-year age means moon formation can still be ongoing long after the planets have opened their common gap.
The same torque-depletion argument predicts that the inner companion PDS 70 b should have a more depleted or already processed circumplanetary reservoir, consistent with the absence of a comparably secure millimeter source at b.
SR 12 c shows that a circumplanetary disk can survive after planetary mass growth is effectively complete, since its growth timescale is about $1.9\times10^9$ yr, separating disk survival from planet assembly.
The two detections lie close to the extrapolated young-disk continuum flux–host-mass relation, so planetary-mass disks are not intrinsically mass-depleted relative to disks around stars.
The observed circumplanetary disk radius favors late gap-fed inflow over compact pre-gap circularization, implying that the angular momentum of inflow, not the Hill radius alone, sets the moon-forming disk scale.

Reading between the lines

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

If the optically thick ring interpretation holds, the actual dust reservoir could exceed the optically thin Callisto-mass estimate, making PDS 70 c an even more massive moon-formation site than the paper's nominal comparison suggests.
The model's timescale bracket implies that regular-satellite systems may form asynchronously, with inner moons completing around 1 million years and outer moons taking about 10 million years; PDS 70 b and c could be a live example of that asynchrony.
A direct test would be high-resolution molecular-line mapping of gas inside PDS 70 c's Hill sphere: a detected Keplerian gas disk would confirm the reservoir, while a strict gas upper limit would weaken the moon-forming interpretation.
If the system age were revised upward toward or beyond the Iapetus timescale, the same observations would instead suggest a late-surviving remnant rather than an active moon factory.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: this is a better paper than the abstract makes it look. The observational synthesis is careful, the radiative-transfer limits are clean, and the paper is unusually explicit about which inputs are illustrative. The load-bearing weakness is the age-bracketing argument: the ~1e6 yr Callisto and ~1e7 yr Iapetus timescales come straight from the author's own 2003 model and are used to say PDS 70's 5.4±1.0 Myr supports that model. That is circular until those timescales are re-derived in PDS 70-like parameters or independently corroborated. Shift either by an order of magnitude and the bracketing collapses.

What's actually new: the one-zone common-gap depletion calculation, the 578-trajectory ballistic angular-momentum ensemble mapping inflow to r_c, and the explicit placement of PDS 70's age between the two satellite-formation timescales. The dust-mass comparison to Callisto and the 0.88-mm disk-host sequence placement—including the SR 12 c distance/mass revision—are useful, reproducible checks. The author separates optically thin and thick limits cleanly and refuses to claim a CPD gas mass from data that don't provide one. The numerical checks in Appendix C (normalization residuals, resolution convergence) are real evidence of careful bookkeeping.

Soft spots, in proportion: the gap-depletion model uses uncalibrated closure parameters (C_H, C_T, h, η_w), so t_dep ~ few 1e3 yr is illustrative, as admitted. The bigger concern is Section 7.2: the two timescales that carry the central claim are asserted from self-cites with no re-derivation and no argument that circumjovian/circum-Saturnian numbers transfer to PDS 70 c. The paper even contains the ingredients to make that connection—Section 5's surface-density model and Table 3's parameter set—but doesn't do it. Given that, the abstract's 'strong support' overstates what the evidence supports; 'consistent with' is more accurate.

I checked the specific arithmetic the stress-test note flags. The SR 12 c growth-time, the 0.58–0.66 au emitting radii, and the ballistic angular-momentum bookkeeping all hold. This is not a paper full of invented precision; it is a transparent exploratory synthesis with one over-extended conclusion.

Bottom line: it deserves serious refereeing. A referee should ask for either a re-derivation of the clearing timescales applied to PDS 70 c parameters or a softened conclusion, and for calibration of C_H/f_ret. I would read it closely and cite the r_c ≈ R_H/3 argument and the disk-host sequence analysis.

Referee Report

2 major / 4 minor

Summary. This paper interprets the ALMA 855-µm and 0.88-mm continuum detections around PDS 70 c and SR 12 c as circumplanetary disks and uses them to argue for a quiescent, solids-enhanced satellite-formation environment. In the optically thin limit the authors derive a dust mass of 0.007–0.031 M⊕ at 26 K; in the optically thick limit they derive a minimum coplanar emitting radius of 0.58–0.66 au depending on temperature. They show that this scale is much larger than the pre-gap circularization radius RH/48 and is consistent with gap-fed inflow at rc~RH/3, and they use a finite-common-gap depletion model to motivate late-stage delivery of gas and solids into the circumplanetary region. For SR 12 c they compute a mass-growth timescale of (1.9±0.5)×10^9 yr, concluding that a gas-bearing and solids-bearing circumplanetary disk can survive after planetary growth is effectively complete. The central chronometric claim is that the 5.4±1.0 Myr age of PDS 70 lies between the model's ~10^6 yr Callisto and ~10^7 yr Iapetus formation timescales, which is presented as strong support for the authors' satellite-formation model.

Significance. The paper has real strengths: the optically thin and optically thick continuum inversions are standard and clean; the kinematic relation rc = λ² RH/3 is parameter-free; the SR 12 c growth-time arithmetic is transparent; and the manuscript is unusually honest in labeling model inputs as illustrative (Table 3) and in reporting numerical residual checks (Appendix C). If the chronometric argument could be made quantitative, the paper would establish that the two secure cold planetary-mass circumplanetary disk detections are consistent with late-stage, gap-fed, quiet satellite formation and that such disks can outlive planetary growth. As it stands, the significance is lower than the abstract claims, because the decisive chronological bracket is imported from earlier work rather than derived or transferred to the PDS 70 c parameters in this manuscript.

major comments (2)

[§7.2 and Conclusion item 5] The central chronometric claim—that the 5.4±1.0 Myr age of PDS 70 lies between the ~10^6 yr Callisto and ~10^7 yr Iapetus formation timescales—rests entirely on gas-drag clearing timescales imported from Mosqueira & Estrada (2003a,b), Estrada et al. (2009), and Mosqueira et al. (2010b). The manuscript states that these are outputs of a clearing calculation but does not reproduce that calculation or exhibit its dependence on circumplanetary gas surface density, satellitesimal size, and local orbital period. It also does not argue why timescales calibrated to the circumjovian and circum-Saturnian disks should transfer to PDS 70 c, whose planet mass (4–12 MJ), Hill radius (4.1–5.9 au), CPD radius (0.6–1.2 au), and gap-fed supply history all differ. The manuscript itself supplies the CPD surface-density model in Section 5 and a PDS 70 c parameter set in Table 3, but never connects them to the imported clearing timescale. A factor-of-few change in the drag timescale moves the bracket outside the 4.4–6.4 Myr window, so the 'strong support' conclusion in the abstract is not currently supported by the evidence presented. This can be fixed by deriving the clearing timescale for the PDS 70 c parameters or by clearly re-scoping the claim to consistency rather than timing.
[§4.2–§5] The temporal bookkeeping behind the age comparison is incomplete. The one-zone depletion model gives t_dep ≈ (2.1–5.4)×10^3 yr for PDS 70 (Eq. 52), and Section 5 imposes the phase switch t_gap = t_dep (Eq. 56) for the late gap-fed supply. With these values, the Hill-supply rate at 5.4 Myr is e^{-5.4×10^6 / 3×10^3} ≈ 0, so the continuum source observed today cannot be fed by the modeled late inflow unless t_dep is much longer or the switch to gap-fed supply occurs at a much later absolute time. The paper does not state the absolute zero-point of t relative to the stellar age, nor does it justify measuring the 5.4 Myr age from the beginning of the satellite-forming phase. The statement that the PDS 70 age 'lies between' the Callisto and Iapetus timescales therefore depends on unstated assumptions about when that phase began. The manuscript should either define the relation between model time and observed age or restrict the chronological conclusion to consistency.

minor comments (4)

[§2.4, Eq. (14)] Equation (14) is typeset as a hanging list of symbols and is not a coherent equation; it should be rewritten as an explicit sentence stating that M_g,c, Σ_g,c(R), and (M_g/M_d)_c are not directly measured.
[§2.4 and §7.2] The absence of a secure continuum detection at PDS 70 b is used as evidence for a more depleted inner reservoir, but no quantitative upper limit on b's dust mass or emitting area is derived; the non-detection should be presented as a tentative constraint, not as independent support for the model.
[Appendix D] Appendix D documents a process-level issue with AI-assisted reasoning rather than contributing to the scientific argument; it would be more appropriate as a brief note in the acknowledgments or as a separate editorial remark, and its presence in the scientific body is distracting.
[Figure 1] Figure 1 quotes single Hill radii for PDS 70 b and c (2.81 au and 5.05 au), while the text adopts a 4–12 MJ mass range for c that gives RH = 4.1–5.9 au; using a representative value is fine, but the figure should either state the assumed masses or show the range.

Circularity Check

1 steps flagged · score 4.0 of 10

The age-bracketing argument that carries the 'strong support' conclusion is imported from the author's own prior gas-drag-clearing model, while the dust-mass and radial-scale comparisons are independent.

self citation load bearing [Abstract; Section 7.2 (Satellite assembly, disk clearing, and the age of PDS 70); Conclusion item 5; Table 2]
"These observations are consistent with our satellite formation model for Jupiter and Saturn (Mosqueira & Estrada 2003a,b, submitted in 2001), in which gas-drag clearing of satellitesimals gives formation timescales of ∼10^6 yr for Callisto and ∼10^7 yr for Iapetus. The PDS 70 age of 5.4±1.0 Myr lies between these values. These constraints provide strong support for a quiescent, solids-enhanced satellite-forming environment..."

The two bracketing timescales (∼10^6 yr for Callisto, ∼10^7 yr for Iapetus) are not derived anywhere in this manuscript. They are quoted as outputs of Mosqueira & Estrada (2003a,b), Estrada et al. (2009), and Mosqueira et al. (2010b), all self-authored prior work, and Section 7.2 explicitly cites them as outputs of the gas-drag clearing calculation. No transfer argument is given for why circumjovian/circum-Saturnian clearing timescales apply to PDS 70 c, whose mass, CPD radius, gas surface density, and gap-fed supply history differ. The abstract and Conclusion item 5 then use the age lying between these two self-cited values as the central support for the satellite-formation model.

full rationale

The main observational inputs are genuinely external to the model under test: the 855-µm flux and distance, the 0.6–1.2 au emitting scale, the spectral index, and the SR 12 c accretion rate come from Benisty et al. (2021), Domínguez-Jamett et al. (2025), Finley et al. (2026), and other cited surveys. The optically thin dust mass (0.007–0.031 M⊕) is compared directly to Callisto's mass (0.018 M⊕), and the 0.88-mm disk–host sequence is an independent empirical relation; neither of these comparisons is constructed from the author's satellite-formation model. The one load-bearing self-citation is the paired satellitesimal gas-drag clearing timescale (∼10^6 yr for Callisto, ∼10^7 yr for Iapetus) that brackets the PDS 70 age. These numbers are imported from the author's own prior papers without re-derivation, and no quantitative connection is made between the paper's own PDS 70 c CPD parameter set and those clearing timescales. Consequently the abstract's 'strong support' conclusion leans on an age bracket whose endpoints are self-cited model outputs, which is a partial circularity in the evidential sense. The paper's own acknowledged limitations (unresolved retention fraction f_ret, imposed t_gap = t_dep, no measured CPD gas mass) weaken the strength of the claims but are not themselves circular steps. Overall, the dust-mass and radial-scale evidence are independent, so the paper is not wholly circular; the circularity score is 4 rather than higher because the central claim still has substantial non-circular content.

Assumptions & free parameters 11 free parameters · 6 assumptions · 0 invented entities

The central comparison rests on a chain of adopted closure coefficients (C_T, C_H, h, eta_w), an imposed phase switch, an unresolved retention fraction, and the prior satellite-formation timescales. The observational masses and radii are external benchmarks, but the support claimed for the satellite model is conditional on these choices.

free parameters (11)

disk aspect ratio h_b=h_c = 0.05
Illustrative closure value in the gap-torque calculation; directly sets the gap-opening timescales in Equations 49 to 52.
torque coefficient C_T = 0.01
Adopted dimensionless torque coefficient in Equation 38; no three-dimensional calibration; directly sets t_clear.
Hill transfer coefficient C_H = 0.1
Chosen value for net Hill-region transfer in Equation 40; the paper itself states three-dimensional simulations are required to calibrate it.
clearing half-width eta_w = 2.5
Nonlinear horseshoe half-width from Masset et al. 2006; used as a bookkeeping width in Equation 39, not a measured gap edge.
initial common-gap reservoir mass M_gap,0 = 5 M_J
Illustrative normalization used for the all-retained late circumplanetary mass upper bound in Equation 57.
retained gas fraction f_ret = 1 (upper bound)
Sets the late circumplanetary gas mass; unresolved and explicitly stated; the fiducial M_late=0.068 M_J is an all-retained upper bound.
PDS 70 c fiducial mass M_c = 7.5 M_J
Chosen within the 4 to 12 M_J interval from Shibaike et al. 2026; affects R_H and both r_c values.
phase switch time t_gap = t_dep
Imposed transition time between pre-gap and gap-fed inflow; the paper states it is not derived from the depletion solution.
ballistic entry velocity ranges and interaction radius = 0.1<=u_n<=0.5, |u_t|<=0.1, S_sh=0.5 R_H
Chosen low-relative-velocity L1/L2 entry ensemble; sets the flux-weighted lambda=0.87 and the predicted circularization radius.
inflow mechanical conversion efficiency epsilon_in = 1e-3
Effective conversion efficiency for circumplanetary disk forcing in Appendix A; illustrative only.
stress closure coefficients C_epsilon, l, b_kappa_t = 1, 0.5H, 0.01
Coefficients for the K^(3/2) cascade closure used in Figures 7 and 8; chosen for illustration.

assumptions (6)

domain assumption The one-sided tidal torque formula |T|=C_T q^2 Sigma a^4 Omega^2 h^-3 applies to partial gaps in a shared reservoir.
Used in the finite-reservoir depletion model in Section 4.1, Equation 38; standard in the gap-opening literature but assumes a torque scaling that may not hold for two planets sharing one gap.
domain assumption Net Hill-sphere mass flux is approximated by Mdot_H = C_H Sigma Omega R_H^2 with a single coefficient.
Section 4.1, Equation 40; the paper notes the coefficient includes unresolved inflow and recycling and requires three-dimensional calibration.
domain assumption The circumplanetary disk is coplanar with the circumstellar disk at inclination i=51.7 degrees.
Section 2.3.2; coplanarity is assumed, not measured; the physical radius conversion scales as 1/sqrt(cos i).
domain assumption The gas-drag clearing timescales of the solids-enhanced minimum-mass model (Callisto about 1e6 yr, Iapetus about 1e7 yr) are correct and transferable to PDS 70.
Section 7.2; these timescales come from the author's prior papers and are not re-derived or independently verified in this manuscript; they anchor the age comparison.
domain assumption Keplerian shear with Coriolis coupling prevents sustained turbulence in unforced circumplanetary disks.
Appendix A and Section 1 rely on Balbus and Hawley 1998 and Hawley et al. 1999; this is a contested physical claim central to the quiescence argument.
domain assumption A planar ensemble of 578 L1/L2 trajectories approximates the mass-flux-weighted angular momentum of three-dimensional Hill-sphere inflow.
Section 5; used to obtain lambda=0.87 and the circularization radius distribution; vertical entry, recycling, and retention are not modeled.

how reviews work

0 comments

Cite this review

Pith. "Pith review of PDS 70 c and SR 12 c: Observational Constraints on Giant-Planet and Satellite Formation." pith.science (2026). https://pith.science/paper/MKQZLMX5

@misc{pith2026260810409,
  author       = {Pith},
  title        = {Pith review of: PDS 70 c and SR 12 c: Observational Constraints on Giant-Planet and Satellite Formation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MKQZLMX5}},
  note         = {Machine review of arXiv:2608.10409}
}

abstract

PDS~70~c and SR~12~c are the only bound planetary-mass objects with secure cold submillimeter disk detections. Together they constrain giant-planet growth and satellite formation. The PDS~70 planets exhibit remarkable parallels to the Jupiter--Saturn pair in our Solar System. Both PDS~70 planets accrete within one shared gap, which links their final masses, the material reaching each Hill sphere, and the properties of the circumplanetary disk. Planetary torques deplete this finite reservoir, causing circumplanetary supply to decline as the protoplanets open a circumstellar gap. SR~12~c separates the planetary-growth and satellite-formation timescales: gas and solids survive even though its current mass-growth timescale is $(1.9\pm0.5)\times10^9$~yr. For PDS~70~c, the 855-$\mu$m flux implies $0.007$--$0.031\,\Mearth$ of dust at 26~K in the optically thin limit, while the optically thick limit requires a minimum coplanar radius of $0.58$--$0.66$~au, depending on temperature. This scale is compatible with late-stage gas inflow through a well-formed gap with specific angular momentum, $r_{\rm c}\sim\RH/3$. These observations are consistent with our satellite formation model for Jupiter and Saturn (Mosqueira \& Estrada 2003a,b, submitted in 2001), in which gas-drag clearing of satellitesimals gives formation timescales of $\sim10^6$~yr for Callisto and $\sim10^7$~yr for Iapetus. The PDS~70 age of $5.4\pm1.0$~Myr lies between these values. These constraints provide strong support for a quiescent, solids-enhanced satellite-forming environment, coupled in the early stages to planetary-gap evolution.

Figures

Figures reproduced from arXiv: 2608.10409 by the authors.

**Figure 1.** Radial architecture of Jupiter–Saturn and PDS 70 b–c. A compact millimeter continuum source is robustly associated with PDS 70 c. Recent Band 6 analyses contain tentative emission near PDS 70 b, but there is still no comparably secure multiband CPD detection at b. give the two-point spectral index Fν ∝ ν α , αB4,B7 = 2.01 ± 0.22, (1) where Fν is the flux density at observing frequency ν and α is the spectral index.… view at source ↗

**Figure 2.** Multiwavelength continuum measurements at PDS 70 c. Detections and upper limits are from [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Optically thin 855-µm dust mass as a function of the adopted dust temperature, calculated with the nominal 86 µJy flux and 112.4-pc distance used by Benisty et al. (2021). The curves use their 1-µm and 1-mm grain opacities, κ855 = 0.79 and 3.63 cm2 g −1 , respectively; their adopted 26-K temperature gives 0.031 and 0.0068 M⊕, the latter reported as approximately 0.007 M⊕. The measured flux uncertainty is ±16 µJy … view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: The 0.88-mm disk flux–host-mass relation extended into the planetary-mass regime. The solid line and shaded region are the young-disk relation and its 0.74-dex intrinsic scatter from Wu et al. (2020), with all fluxes scaled to 140 pc using Equation (15). Downward trian…

**Figure 5.** Figure 5: Hill and centrifugal-radius scalings for PDS 70 c. The pre-gap Lissauer estimate gives rc = RH/48, whereas low-relative-velocity inflow through the L1/L2 regions of a developed gap gives rc ∼ RH/3. The shaded horizontal interval is the approximately 0.58–1.2 au physic…

**Figure 6.** Figure 6: Radial deposition profile from the late gap-fed ballistic ensemble for the all-retained illustrative normalization, Mgap,0 = 5 MJ and fret = 1. The dotted line marks the compact RH/48 pre-gap scale, the dashed line the late flux-weighted mean circularization radius, a…

**Figure 7.** Figure 7: Conditional inflow-depth scalings for the inputs in [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

**Figure 8.** Figure 8: Reduced CPD stress response driven by the torque-depleted common-gap reservoir. Panel (a) shows the calculated Hill supply; the HST-derived planetary accretion band is a comparison only. Panels (b) and (c) show the vertical response and its density-weighted averages fo…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

105 extracted references · 25 canonical work pages

[2]

and Benisty, M

Isella, A. and Benisty, M. and Teague, R. and Bae, J. and Keppler, M. and Facchini, S. and P. Detection of Continuum Submillimeter Emission Associated with Candidate Protoplanets , journal =. 2019 , volume =

2019
[3]

and others , title =

Keppler, M. and others , title =. Astronomy & Astrophysics , year =
[4]

Haffert, S. Y. and others , title =. Nature Astronomy , year =
[5]

Orbital and Atmospheric Characterization of the Planet within the Gap of the PDS 70 Transition Disk , journal =

M. Orbital and Atmospheric Characterization of the Planet within the Gap of the PDS 70 Transition Disk , journal =. 2018 , volume =

2018
[6]

Wang, J. J. and others , title =. The Astronomical Journal , year =
[14]

Liu, H. B. and Doi, K. and Casassus, S. and Kataoka, A. and Dong, R. and Hashimoto, J. and Weber, P. , title =. Astronomy & Astrophysics , year =. 2602.05247 , archivePrefix =

arXiv
[18]

and others , title =

Portilla-Revelo, B. and others , title =. Astronomy & Astrophysics , year =
[19]

and Estrada, P

Mosqueira, I. and Estrada, P. R. , title =. Icarus , year =

Show all 105 references

[21]

and Estrada, P

Mosqueira, I. and Estrada, P. R. and Turrini, D. , title =. Space Science Reviews , year =
[22]

Estrada, P. R. and Mosqueira, I. , title =. Icarus , year =
[23]

and Estrada, P

Mosqueira, I. and Estrada, P. R. and Charnoz, S. , title =. Icarus , year =
[24]

and Morbidelli, A

Batygin, K. and Morbidelli, A. , title =. The Astrophysical Journal , year =
[25]

Dust Evolution and Satellitesimal Formation in Circumplanetary Disks , journal =

Dr. Dust Evolution and Satellitesimal Formation in Circumplanetary Disks , journal =. 2018 , volume =

2018
[26]

and Johansen, A

Ronnet, T. and Johansen, A. , title =. Astronomy & Astrophysics , year =
[27]

and others , title =

Nimmo, F. and others , title =. Space Science Reviews , year =
[28]

and others , title =

Blanc, M. and others , title =. Space Science Reviews , year =
[33]

Fujii, Y. I. and Okuzumi, S. and Tanigawa, T. and Inutsuka, S.-i. , title =. The Astrophysical Journal , year =. 1402.6091 , archivePrefix =

arXiv
[34]

Shakura, N. I. and Sunyaev, R. A. , title =. Astronomy & Astrophysics , year =
[35]

and Pringle, J

Lynden-Bell, D. and Pringle, J. E. , title =. Monthly Notices of the Royal Astronomical Society , year =
[36]

and Morbidelli, A

Crida, A. and Morbidelli, A. and Masset, F. , title =. Icarus , year =
[37]

and others , title =

Bae, J. and others , title =. The Astrophysical Journal Letters , year =
[38]

Walsh, K. J. and Morbidelli, A. and Raymond, S. N. and O'Brien, D. P. and Mandell, A. M. , title =. Nature , year =
[39]

Dempsey, A. M. and Lee, W.-K. and Lithwick, Y. , title =. The Astrophysical Journal Letters , year =
[41]

and Federrath, C

Schmidt, W. and Federrath, C. , title =. Astronomy & Astrophysics , year =
[43]

and others , title =

Birnstiel, T. and others , title =. The Astrophysical Journal Letters , year =
[44]

Ormel, C. W. and Cuzzi, J. N. , title =. Astronomy & Astrophysics , year =
[45]

Youdin, A. N. and Lithwick, Y. , title =. Icarus , year =
[46]

and Youdin, A

Li, R. and Youdin, A. N. , title =. The Astrophysical Journal , year =
[47]

Safronov, V. S. , title =
[48]

, title =

Mordasini, C. , title =. Handbook of Exoplanets , editor =. 2018 , pages =

2018
[49]

Lissauer, J. J. , title =. Icarus , year =
[52]

and Burin, M

Ji, H. and Burin, M. and Schartman, E. and Goodman, J. , title =. Nature , year =. doi:10.1038/nature05323 , eprint =

doi
[53]

Balbus, S. A. and Hawley, J. F. , title =. Reviews of Modern Physics , year =
[54]

Shear-improved Smagorinsky Model for Large-eddy Simulation of Wall-bounded Turbulent Flows , journal =

L. Shear-improved Smagorinsky Model for Large-eddy Simulation of Wall-bounded Turbulent Flows , journal =. 2007 , volume =

2007
[58]

and Tremaine, S

Goldreich, P. and Tremaine, S. , title =. The Astrophysical Journal , year =
[60]

and Johansen, A

Paardekooper, S.-J. and Johansen, A. , title =. Space Science Reviews , year =
[61]

and Laibe, G

Dipierro, G. and Laibe, G. , title =. Monthly Notices of the Royal Astronomical Society , year =
[73]

, title =

Hayes, Wallace D. , title =. Journal of Fluid Mechanics , year =
[74]

Kevlahan, N. K.-R. , title =. Journal of Fluid Mechanics , year =
[75]

Kevlahan, N. K.-R. and Pudritz, R. E. , title =. The Astrophysical Journal , year =
[76]

and Brandenburg, A

Del Sordo, F. and Brandenburg, A. , title =. Astronomy & Astrophysics , year =. doi:10.1051/0004-6361/201015661 , eprint =

doi
[77]

and Hartmann, L

Bae, J. and Hartmann, L. and Zhu, Z. , title =. The Astrophysical Journal , year =. doi:10.1088/0004-637X/805/1/15 , eprint =

doi
[78]

and Bae, J

Kuznetsova, A. and Bae, J. and Hartmann, L. and Mac Low, M.-M. , title =. The Astrophysical Journal , year =. doi:10.3847/1538-4357/ac54a8 , eprint =

doi
[79]

and Schmidt, W

Iapichino, L. and Schmidt, W. and Niemeyer, J. C. and Merklein, J. , title =. Monthly Notices of the Royal Astronomical Society , year =. doi:10.1111/j.1365-2966.2011.18550.x , eprint =

2011
[82]

Rosenthal, M. M. and Chiang, E. I. and Ginzburg, S. and Murray-Clay, R. A. , title =. Monthly Notices of the Royal Astronomical Society , year =
[86]

M., et al

Bae, J., Teague, R., Andrews, S. M., et al. 2022, The Astrophysical Journal Letters, 934, L20, 10.3847/2041-8213/ac7fa3

2022 doi
[87]

A., & Hawley, J

Balbus, S. A., & Hawley, J. F. 1998, Reviews of Modern Physics, 70, 1, 10.1103/RevModPhys.70.1

1998 doi
[88]

2021, The Astrophysical Journal Letters, 916, L2, 10.3847/2041-8213/ac0f83

Benisty, M., et al. 2021, The Astrophysical Journal Letters, 916, L2, 10.3847/2041-8213/ac0f83

2021 doi
[89]

2018, The Astrophysical Journal Letters, 869, L45

Birnstiel, T., et al. 2018, The Astrophysical Journal Letters, 869, L45

2018
[90]

2026, Astronomy & Astrophysics, 710, L10, 10.1051/0004-6361/202659553

Casassus, S., C \'a rcamo, M., Dom \'i nguez-Jamett, O., et al. 2026, Astronomy & Astrophysics, 710, L10, 10.1051/0004-6361/202659553

2026 doi
[91]

2023, Monthly Notices of the Royal Astronomical Society, 525, 2806, 10.1093/mnras/stad2269

Choksi, N., Chiang, E., Fung, J., & Zhu, Z. 2023, Monthly Notices of the Royal Astronomical Society, 525, 2806, 10.1093/mnras/stad2269

2023 doi
[92]

J., & Rafikov, R

Cordwell, A. J., & Rafikov, R. R. 2024, Monthly Notices of the Royal Astronomical Society, 534, 1394, 10.1093/mnras/stae2089

2024 doi
[93]

2006, Icarus, 181, 587

Crida, A., Morbidelli, A., & Masset, F. 2006, Icarus, 181, 587

2006
[94]

Cugno, G., & Grant, S. L. 2025, The Astrophysical Journal Letters, 991, L46, 10.3847/2041-8213/ae0290

2025 doi
[95]

2024, The Astrophysical Journal Letters, 966, L21, 10.3847/2041-8213/ad3cbc

Cugno, G., Patapis, P., Banzatti, A., et al. 2024, The Astrophysical Journal Letters, 966, L21, 10.3847/2041-8213/ad3cbc

2024 doi
[96]

2017, Monthly Notices of the Royal Astronomical Society, 469, 1932, 10.1093/mnras/stx977

Dipierro, G., & Laibe, G. 2017, Monthly Notices of the Royal Astronomical Society, 469, 1932, 10.1093/mnras/stx977

2017 doi
[97]

B., et al

Doi, K., Kataoka, A., Liu, H. B., et al. 2024, The Astrophysical Journal Letters, 974, L25, 10.3847/2041-8213/ad7f51

2024 doi
[98]

2025, Astronomy & Astrophysics, 702, A18, 10.1051/0004-6361/202554485

Dom \'i nguez-Jamett, O., et al. 2025, Astronomy & Astrophysics, 702, A18, 10.1051/0004-6361/202554485

2025 doi
[99]

R., & Mosqueira, I

Estrada, P. R., & Mosqueira, I. 2006, Icarus, 181, 486, 10.1016/j.icarus.2005.11.006

2006 doi
[100]

R., Mosqueira, I., Lissauer, J

Estrada, P. R., Mosqueira, I., Lissauer, J. J., D'Angelo, G., & Cruikshank, D. P. 2009, in Europa, ed. R. T. Pappalardo, W. B. McKinnon, & K. K. Khurana (Tucson: University of Arizona Press), 27--58. 0809.1418

2009 arXiv
[101]

2025, Astronomy & Astrophysics, 699, A373, 10.1051/0004-6361/202554959

Fasano, D., et al. 2025, Astronomy & Astrophysics, 699, A373, 10.1051/0004-6361/202554959

2025 doi
[102]

O., Bowler, B

Finley, C. O., Bowler, B. P., Wu, Y.-L., et al. 2026, The Astronomical Journal, 10.3847/1538-3881/ae7a39

2026 doi
[103]

M., et al

Flaherty, K. M., et al. 2020, The Astrophysical Journal, 895, 109, 10.3847/1538-4357/ab8cc5

2020 doi
[104]

2019, The Astrophysical Journal, 887, 152, 10.3847/1538-4357/ab53da

Fung, J., Zhu, Z., & Chiang, E. 2019, The Astrophysical Journal, 887, 152, 10.3847/1538-4357/ab53da

2019 doi
[105]

1980, The Astrophysical Journal, 241, 425, 10.1086/158356

Goldreich, P., & Tremaine, S. 1980, The Astrophysical Journal, 241, 425, 10.1086/158356

1980 doi
[106]

Y., et al

Haffert, S. Y., et al. 2019, Nature Astronomy, 3, 749, 10.1038/s41550-019-0780-5

2019 doi
[107]

F., Balbus, S

Hawley, J. F., Balbus, S. A., & Winters, W. F. 1999, The Astrophysical Journal, 518, 394, 10.1086/307282

1999 doi
[108]

Hoch, K. K. W., Rowland, M., Petrus, S., et al. 2025, Nature, 643, 938, 10.1038/s41586-025-09174-w

2025 doi
[109]

N., & Dullemond, C

H \"u hn, L.-A., Kimmig, C. N., & Dullemond, C. P. 2026, Astronomy & Astrophysics, 708, A93, 10.1051/0004-6361/202558773

2026 doi
[110]

F., Bae, J., Galloway-Sprietsma, M., et al

Izquierdo, A. F., Bae, J., Galloway-Sprietsma, M., et al. 2026, The Astrophysical Journal Letters, 997, L2, 10.3847/2041-8213/ae2f59

2026 doi
[111]

2018, Astronomy & Astrophysics, 617, A44, 10.1051/0004-6361/201832957

Keppler, M., et al. 2018, Astronomy & Astrophysics, 617, A44, 10.1051/0004-6361/201832957

2018 doi
[112]

2019, Astronomy & Astrophysics, 625, A118, 10.1051/0004-6361/201935034

---. 2019, Astronomy & Astrophysics, 625, A118, 10.1051/0004-6361/201935034

2019 doi
[113]

2020, Monthly Notices of the Royal Astronomical Society, 492, 1385, 10.1093/mnras/stz3495

Kretschmer, M., & Teyssier, R. 2020, Monthly Notices of the Royal Astronomical Society, 492, 1385, 10.1093/mnras/stz3495

2020 doi
[114]

J., et al

Law, C. J., et al. 2024, The Astrophysical Journal, 964, 190. 2401.03018

2024 arXiv
[115]

Li, Y.-P., Chen, Y.-X., & Lin, D. N. C. 2023, Monthly Notices of the Royal Astronomical Society, 526, 5346, 10.1093/mnras/stad3049

2023 doi
[116]

Lissauer, J. J. 1995, Icarus, 114, 217, 10.1006/icar.1995.1057

1995
[117]

L., et al

M \^a lin, M., Ward-Duong, K., Grant, S. L., et al. 2025, Astronomy & Astrophysics, 704, A181. 2510.07253

2025
[118]

S., D'Angelo, G., & Kley, W

Masset, F. S., D'Angelo, G., & Kley, W. 2006, The Astrophysical Journal, 652, 730, 10.1086/507515

2006 doi
[119]

Mosqueira, I., & Estrada, P. R. 2003 a , Icarus, 163, 198, 10.1016/S0019-1035(03)00076-9

2003 doi
[120]

2003 b , Icarus, 163, 232, 10.1016/S0019-1035(03)00077-0

---. 2003 b , Icarus, 163, 232, 10.1016/S0019-1035(03)00077-0

2003 doi
[121]

R., & Charnoz, S

Mosqueira, I., Estrada, P. R., & Charnoz, S. 2010 a , Icarus, 207, 448

2010
[122]

R., & Turrini, D

Mosqueira, I., Estrada, P. R., & Turrini, D. 2010 b , Space Science Reviews, 153, 431

2010
[123]

2018, Astronomy & Astrophysics, 617, L2, 10.1051/0004-6361/201833584

M \"u ller, A., et al. 2018, Astronomy & Astrophysics, 617, L2, 10.1051/0004-6361/201833584

2018 doi
[124]

2018, Space Science Reviews, 214, 38, 10.1007/s11214-018-0472-y

Paardekooper, S.-J., & Johansen, A. 2018, Space Science Reviews, 214, 38, 10.1007/s11214-018-0472-y

2018 doi
[125]

M., et al

Patapis, P., Morales-Calder \'o n, M., Arabhavi, A. M., et al. 2025, Astronomy & Astrophysics, 704, A5, 10.1051/0004-6361/202556296

2025 doi
[126]

2016, The Astrophysical Journal, 816, 25, 10.3847/0004-637X/816/1/25

Pinte, C., et al. 2016, The Astrophysical Journal, 816, 25, 10.3847/0004-637X/816/1/25

2016 doi
[127]

P., & Ormel, C

Popovas, A., Nordlund, ., Ramsey, J. P., & Ormel, C. W. 2018, Monthly Notices of the Royal Astronomical Society, 479, 5136, 10.1093/mnras/sty1752

2018 doi
[128]

2023, Astronomy & Astrophysics, 677, A76, 10.1051/0004-6361/202346607

Portilla-Revelo, B., Kamp, I., Facchini, S., et al. 2023, Astronomy & Astrophysics, 677, A76, 10.1051/0004-6361/202346607

2023 doi
[129]

C., & Trilling, D

Quillen, A. C., & Trilling, D. E. 1998, The Astrophysical Journal, 508, 707, 10.1086/306421

1998 doi
[130]

Rafikov, R. R. 2002, The Astrophysical Journal, 572, 566, 10.1086/340228

2002 doi
[131]

2024, Astronomy & Astrophysics, 689, A65, 10.1051/0004-6361/202449698

Rampinelli, L., et al. 2024, Astronomy & Astrophysics, 689, A65, 10.1051/0004-6361/202449698

2024 doi
[132]

2020, Astronomy & Astrophysics, 633, A93

Ronnet, T., & Johansen, A. 2020, Astronomy & Astrophysics, 633, A93

2020
[133]

M., Chiang, E

Rosenthal, M. M., Chiang, E. I., Ginzburg, S., & Murray-Clay, R. A. 2020, Monthly Notices of the Royal Astronomical Society, 498, 2054, 10.1093/mnras/staa1721

2020 doi
[134]

2011, Astronomy & Astrophysics, 528, A106

Schmidt, W., & Federrath, C. 2011, Astronomy & Astrophysics, 528, A106

2011
[135]

2024, Astronomy & Astrophysics, 687, A166, 10.1051/0004-6361/202449522

Shibaike, Y., & Mordasini, C. 2024, Astronomy & Astrophysics, 687, A166, 10.1051/0004-6361/202449522

2024 doi
[136]

2026, arXiv e-prints

Shibaike, Y., Okuzumi, S., Ueda, T., Doi, K., & Fukagawa, M. 2026, arXiv e-prints. 2607.03866

2026 arXiv
[137]

Tanigawa, T., Ohtsuki, K., & Machida, M. N. 2012, The Astrophysical Journal, 747, 47, 10.1088/0004-637X/747/1/47

2012 doi
[138]

2025, Astronomy & Astrophysics, 698, A19, 10.1051/0004-6361/202553936

Trevascus, D., et al. 2025, Astronomy & Astrophysics, 698, A19, 10.1051/0004-6361/202553936

2025 doi
[139]

2020, Astronomy & Astrophysics, 642, A164, 10.1051/0004-6361/202038087

Villenave, M., et al. 2020, Astronomy & Astrophysics, 642, A164, 10.1051/0004-6361/202038087

2020 doi
[140]

2022, The Astrophysical Journal, 930, 11, 10.3847/1538-4357/ac5fae

---. 2022, The Astrophysical Journal, 930, 11, 10.3847/1538-4357/ac5fae

2022 doi
[141]

P., Lambrechts, M., et al

Villenave, M., Rosotti, G. P., Lambrechts, M., et al. 2025, Astronomy & Astrophysics, 697, A64, 10.1051/0004-6361/202553822

2025 doi
[142]

J., et al

Wang, J. J., et al. 2021, The Astronomical Journal, 161, 148, 10.3847/1538-3881/abdb2d

2021 doi
[143]

P., Sheehan, P

Wu, Y.-L., Bowler, B. P., Sheehan, P. D., et al. 2020, The Astronomical Journal, 159, 229, 10.3847/1538-3881/ab818c

2020 doi
[144]

2022, The Astrophysical Journal Letters, 930, L3, 10.3847/2041-8213/ac6420

---. 2022, The Astrophysical Journal Letters, 930, L3, 10.3847/2041-8213/ac6420

2022 doi
[145]

P., Sanghi, A., et al

Zhou, Y., Bowler, B. P., Sanghi, A., et al. 2025, The Astrophysical Journal Letters, 980, L39, 10.3847/2041-8213/adb134

2025 doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [2]

and Benisty, M

Isella, A. and Benisty, M. and Teague, R. and Bae, J. and Keppler, M. and Facchini, S. and P. Detection of Continuum Submillimeter Emission Associated with Candidate Protoplanets , journal =. 2019 , volume =

2019

[2] [3]

and others , title =

Keppler, M. and others , title =. Astronomy & Astrophysics , year =

[3] [4]

Haffert, S. Y. and others , title =. Nature Astronomy , year =

[4] [5]

Orbital and Atmospheric Characterization of the Planet within the Gap of the PDS 70 Transition Disk , journal =

M. Orbital and Atmospheric Characterization of the Planet within the Gap of the PDS 70 Transition Disk , journal =. 2018 , volume =

2018

[5] [6]

Wang, J. J. and others , title =. The Astronomical Journal , year =

[6] [14]

Liu, H. B. and Doi, K. and Casassus, S. and Kataoka, A. and Dong, R. and Hashimoto, J. and Weber, P. , title =. Astronomy & Astrophysics , year =. 2602.05247 , archivePrefix =

arXiv

[7] [18]

and others , title =

Portilla-Revelo, B. and others , title =. Astronomy & Astrophysics , year =

[8] [19]

and Estrada, P

Mosqueira, I. and Estrada, P. R. , title =. Icarus , year =