Reading between the rings: observed dust ring properties as probes of planet masses

Amena Faruqi; Farzana Meru; Jessica Speedie; Ralph E. Pudritz

arxiv: 2605.27627 · v1 · pith:BUMT2L2Onew · submitted 2026-05-26 · 🌌 astro-ph.EP

Reading between the rings: observed dust ring properties as probes of planet masses

Amena Faruqi , Jessica Speedie , Ralph E. Pudritz , Farzana Meru This is my paper

Pith reviewed 2026-06-29 14:58 UTC · model grok-4.3

classification 🌌 astro-ph.EP

keywords protoplanetary disksdust ringsplanet-disk interactionspebble isolation masshydrodynamical simulationsPDS 70planet mass estimationexoALMA

0 comments

The pith

Dust ring peak locations scale linearly with the Hill radius of the embedded planet.

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

This paper tests the hypothesis that dust rings carved by embedded planets in protoplanetary disks carry measurable signatures of the planet's mass. Two-dimensional hydrodynamical simulations across a range of planet masses and disk aspect ratios show that ring dust mass, width, and especially the radial location of the density peak all vary with planet mass. A confirmed linear relation ties the planet's Hill radius directly to the ring's density peak position. The same relations are then used to estimate masses in real observed disks including PDS 70 and five exoALMA targets. The work also offers a new pressure-gradient definition of the pebble-isolation mass and notes how ring properties change once that threshold is crossed.

Core claim

Simulations of planets between 0.5 and 2 times the pebble-isolation mass demonstrate that the radial location of a dust ring's density peak increases linearly with the planet's Hill radius. Ring width and dust mass increase with planet mass only up to the pebble-isolation mass and then plateau. The radial profile of gas pressure around the ring shows an asymmetry whose sense reverses exactly at the pebble-isolation mass, which the authors redefine as the minimum mass that makes the interior pressure gradient steeper than the exterior one. These scalings are applied to observed rings to constrain planet masses and disk aspect ratios.

What carries the argument

The positive linear relationship between a planet's Hill radius and the radial location of its dust ring's density peak, which directly maps observed ring positions to planet mass.

If this is right

Ring width and dust mass increase with planet mass only up to the pebble-isolation mass and remain constant thereafter.
The sense of asymmetry in the gas pressure gradient around the ring indicates whether the planet lies above or below the pebble-isolation mass.
The new pressure-gradient definition identifies the pebble-isolation mass as the point where the interior gradient first exceeds the exterior gradient.
The linear peak-location relation supplies mass estimates for planets in disks with resolved rings such as PDS 70.
Planetesimal formation efficiency inside the ring is expected to vary with planet mass through changes in ring width and surface density.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same ring-position method could be applied to disks where planets have already been detected by direct imaging to test consistency between independent mass measurements.
Rings produced by mechanisms other than embedded planets would be expected to fall off the linear relation, offering a discriminant between formation channels.
Extending the simulations to include dust back-reaction or vertical structure would show whether the reported linear scaling survives more realistic physics.
The pressure-asymmetry diagnostic could be checked against gas kinematic observations to independently confirm the pebble-isolation threshold in the same disks.

Load-bearing premise

Observed dust rings in real protoplanetary disks are produced by the same embedded-planet mechanism that operates in the two-dimensional hydrodynamical simulations.

What would settle it

An observed dust ring whose measured density-peak location deviates from the linear Hill-radius prediction once an independent planet mass and disk aspect ratio are known would falsify the claimed relationship.

Figures

Figures reproduced from arXiv: 2605.27627 by Amena Faruqi, Farzana Meru, Jessica Speedie, Ralph E. Pudritz.

**Figure 1.** Figure 1: Schematic showing the different ring properties being measured in simulations and how they are defined. identified independently. To identify the ring density peak, we restrict our search to a radial range that we expect to contain the ring, to avoid misidentifying global maxima. Since it has been shown that the outer edge of a dust gap scales with the Hill radius of the planet (e.g. Rosotti et al. 2016), … view at source ↗

**Figure 2.** Figure 2: Time evolution of gas and dust surface densities of the highest planet mass model for each aspect ratio. As the planet mass increases and the inner edge moves outward, the ring peak is pushed outwards by approximately the same extent (shown by the linear trend in the data in both Figures 4 and 5, which have approximately the same slope). However, the ring outer edge location moves inwards relative to the … view at source ↗

**Figure 4.** Figure 4: Locations of the dust ring inner edges against the planets’ Hill radii for all three aspect ratios. The dashed black line indicates the linear fit applied to the data points, stated in Equation 10 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Locations of the dust ring peaks against the planets’ Hill radii for all three aspect ratios. The dashed black line indicates the linear fit applied to the data points, stated in Equation 11. The origin of these "shoulders" is apparent by examining the full 2D images of our simulations, as shown in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 3.** Figure 3: Dust ring widths against planet masses for all three aspect ratios. Vertical dotted lines indicate the pebbleisolation mass for each Stokes value, calculated according to the prescription by Bitsch et al. (2018). The ring widths for the two largest Stokes numbers are constant with increasing planet mass, so overlap. Ring width decreases with increasing planet mass for planet masses below the pebble-isola… view at source ↗

**Figure 6.** Figure 6: Mass contained in dust rings against planet mass for all three aspect ratios. The shaded regions indicate the pebble-isolation mass for each aspect ratio. in the gas, leading to it being the same for all Stokes numbers. The ring inner (and outer) edges are set by the interplay of the outward and inward flow of dust caused by the relative pressure gradients on either side of the pressure maximum in the gas.… view at source ↗

**Figure 7.** Figure 7: Dust-to-gas ratios across the extent of the disc for all three aspect ratios at 1500 orbits. The dashed line indicates the initial dust-to-gas ratio of 10−2 . The dotted line indicates a dust-to-gas ratio of 1, the value typically required to trigger the streaming instability [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

**Figure 8.** Figure 8: Probability of planet formation through the gravitational collapse of a clump formed via the streaming instability at the location of the ring peak, for all three aspect ratios, at 1500 orbits. All models showed a high likelihood of being capable of triggering the streaming instability in a ring. 4.5. Refining our understanding of pebble-isolation theory The difference in the behavior of dust when the pe… view at source ↗

**Figure 9.** Figure 9: Absolute values of the maximum pressure gradient interior and exterior to the pressure maximum plotted against planet mass for all three aspect ratios. The gray box indicates the range of values for the pebble-isolation mass for the Stokes numbers modeled. than is drifting inwards, by producing a steeper positive pressure gradient interior to the pressure maximum. Unlike the first scenario, this does not … view at source ↗

**Figure 10.** Figure 10: For illustrative purposes, a map of the dust continuum emission in the PDS 70 disk (ALMA pipeline image in Band 7 from program 2018.A.00030.S; Benisty et al. 2021). The dashed orange and red ellipses indicate the radial locations of the ring’s shoulder and outer peak that we adopt for our discussion in Section 5.2 (54.5 AU and 74.5 AU in deprojected radius, respectively). The white dashed ellipse repres… view at source ↗

**Figure 11.** Figure 11: Normalised dust density profiles and the ring edges identified in each case. Dots indicate the locations of the peaks and edges identifies for each profile. Top row: hp/rp = 0.05, middle row: hp/rp = 0.06, bottom row: hp/rp = 0.07 [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗

**Figure 12.** Figure 12: Snapshots of the 2D surface density profiles of St=0.2 dust for three different planet masses. All three snapshots are taken at 1500 orbits and are taken from simulations that used an aspect ratio of 0.06. The planets’ locations are marked by red dots. The red dashed circles are centred on the origin and used to highlight azimuthal asymmetries in the left and middle plots. The red circles on the right plo… view at source ↗

read the original abstract

We hypothesise that dust rings in protoplanetary discs formed by an embedded planet should have properties that reflect the planet's mass. We use 2D hydrodynamical simulations of planet-disc interactions to investigate this, focusing on planets ranging 0.5-2.0x the pebble-isolation mass, for three different aspect ratios. We find the ring's dust mass, peak location, and width to correlate with planet mass. We confirm a positive linear relationship between a planet's Hill radius and the location of a ring's density peak and demonstrate how this relationship can be used to constrain planet masses in observed systems by applying it to PDS 70. The dust ring width and mass change with planet mass for planet masses up to the pebble-isolation mass, beyond which they become constant. The steepness of the gas pressure radial profile is asymmetric, with the direction of the asymmetry being determined by whether the planet mass is above or below the pebble-isolation mass. We therefore propose a new way to define the pebble-isolation mass: the minimum planet mass which perturbs the gas enough for the pressure gradient interior to the pressure maximum to exceed the pressure gradient exterior to it. We discuss how our findings could be used to constrain or estimate planet masses from gas or dust observations of discs with measurable substructures and apply our results to 5 discs in the exoALMA sample to estimate planet masses and constrain disc aspect ratios. We also discuss how the potential for planetesimal formation in a ring varies with planet mass.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper derives a linear Hill-radius to dust-peak relation and a pressure-gradient definition of pebble-isolation mass from 2D runs, then applies both to PDS 70 and exoALMA disks.

read the letter

The main new pieces are the reported linear scaling between planet Hill radius and the radial location of the dust density peak, plus the suggestion to mark pebble-isolation mass at the point where the interior gas pressure gradient exceeds the exterior one. They also note that ring mass and width rise with planet mass only up to isolation and then flatten.

The simulations cover planets from 0.5 to 2 times isolation mass at three aspect ratios and produce concrete trends that the authors map onto observed ring properties. The applications to PDS 70 and five exoALMA disks turn those trends into mass and aspect-ratio estimates, which is the part that could see use.

The central assumption is that the rings in real disks are produced by the same embedded-planet mechanism modeled here. The runs do not include snow lines, vortices, or dead-zone edges, so there is no check on whether those channels produce similar peak locations or widths. The 2D setup and narrow parameter choices also leave open how the scalings would shift in 3D or with different dust treatments.

This is for people who model or observe disk substructures and want a quick observational proxy for planet mass. A reader already working on ring-planet connections will find the fits and the sample applications straightforward to test.

The work is grounded enough in the simulations and the data applications to merit referee time, even with the scope limited to one formation channel.

Referee Report

3 major / 2 minor

Summary. The paper uses 2D hydrodynamical simulations of embedded planets (0.5–2.0× pebble-isolation mass, three aspect ratios) to show that dust ring mass, peak location, and width correlate with planet mass. It reports a positive linear relation between planet Hill radius and ring density peak location, proposes a new operational definition of pebble-isolation mass based on asymmetry in the gas pressure gradient, and applies the scaling to estimate planet masses in PDS 70 and five exoALMA disks while discussing implications for planetesimal formation.

Significance. If the planet-induced ring mechanism dominates observed substructures, the reported Hill-radius scaling supplies an observationally accessible route to planet-mass estimates that is independent of gap-depth fitting. The work covers a focused mass range near pebble isolation and multiple aspect ratios, and the new pressure-gradient definition of pebble isolation is a falsifiable, observationally testable proposal. These elements would strengthen the paper’s contribution to disk-planet interaction studies if the underlying assumption is addressed.

major comments (3)

[Simulation setup section] Simulation setup section: numerical resolution, grid size, dust treatment (fluid vs. Lagrangian particles, size distribution, and back-reaction), and boundary conditions are not specified. These choices directly control the reported ring peak location, width, and the slope of the Hill-radius relation, so the central correlations cannot be reproduced or assessed without them.
[Application to PDS 70 and exoALMA sample] Application to PDS 70 and exoALMA sample (results/discussion sections): the linear fit is derived exclusively from planet-induced rings and is then inverted to obtain planet masses. No quantitative test or discussion is provided of how alternative ring-forming mechanisms (snow lines, vortices, dead-zone edges) would shift the peak location, rendering the mass estimates conditional on an untested premise that is load-bearing for the claimed observational application.
[Definition of pebble-isolation mass] Definition of pebble-isolation mass (results section): the new criterion (minimum mass at which the interior pressure gradient exceeds the exterior one) is presented as an improvement, but no direct comparison is made to the conventional definition based on the pebble-trapping efficiency or to the pebble-isolation mass values used to normalize the simulation suite. This leaves the relation between the two definitions unclear.

minor comments (2)

Figure captions should explicitly state the number of simulation runs per aspect ratio and the exact planet-mass grid used to generate the linear fit.
The abstract states the relation is 'positive linear' but does not report the fitted slope, intercept, or R²; these statistics should appear in the main text or a table.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major point below, indicating revisions where appropriate to improve reproducibility, clarify assumptions, and strengthen comparisons.

read point-by-point responses

Referee: [Simulation setup section] Simulation setup section: numerical resolution, grid size, dust treatment (fluid vs. Lagrangian particles, size distribution, and back-reaction), and boundary conditions are not specified. These choices directly control the reported ring peak location, width, and the slope of the Hill-radius relation, so the central correlations cannot be reproduced or assessed without them.

Authors: We agree these parameters are required for reproducibility. The revised manuscript will expand the Simulation setup section with explicit values for grid resolution (radial and azimuthal cells), dust treatment (fluid approximation with specified size bins and back-reaction), and boundary conditions. This addition will enable direct assessment of the reported correlations. revision: yes
Referee: [Application to PDS 70 and exoALMA sample] Application to PDS 70 and exoALMA sample (results/discussion sections): the linear fit is derived exclusively from planet-induced rings and is then inverted to obtain planet masses. No quantitative test or discussion is provided of how alternative ring-forming mechanisms (snow lines, vortices, dead-zone edges) would shift the peak location, rendering the mass estimates conditional on an untested premise that is load-bearing for the claimed observational application.

Authors: We acknowledge the estimates are conditional on the planet-induced ring assumption. The revised discussion will explicitly state this caveat and qualitatively address how alternative mechanisms could alter peak locations. A quantitative test of alternatives lies outside the current simulation suite, but the conditional nature will be emphasized to avoid over-interpretation. revision: partial
Referee: [Definition of pebble-isolation mass] Definition of pebble-isolation mass (results section): the new criterion (minimum mass at which the interior pressure gradient exceeds the exterior one) is presented as an improvement, but no direct comparison is made to the conventional definition based on the pebble-trapping efficiency or to the pebble-isolation mass values used to normalize the simulation suite. This leaves the relation between the two definitions unclear.

Authors: The new pressure-gradient definition is offered as an observationally testable alternative. In revision we will add a direct comparison in the results section, relating the new threshold to conventional pebble-trapping efficiency and to the normalization masses adopted in our runs, thereby clarifying the connection between definitions. revision: yes

Circularity Check

0 steps flagged

No circularity: relations derived from independent hydro simulations and applied externally

full rationale

The paper runs new 2D hydrodynamical simulations across a stated planet-mass range and aspect ratios, measures ring properties (mass, peak location, width) directly from the outputs, and reports an empirical linear correlation between Hill radius and density-peak location. This correlation is then applied to external systems (PDS 70 and exoALMA discs). No quoted step defines a quantity in terms of itself, renames a fitted parameter as a prediction, or reduces the central result to a self-citation chain. The hypothesis that observed rings form via the modeled mechanism is an applicability assumption, not a definitional or self-referential reduction in the derivation itself.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

Abstract-only review yields limited visibility into parameters and assumptions; the listed items are inferred from the stated simulation setup and hypothesis.

free parameters (2)

planet mass range (0.5-2.0 times pebble-isolation mass)
Chosen interval for the simulation suite to probe the correlation regime.
three different aspect ratios
Varied parameter to test dependence of ring properties on disk thickness.

axioms (1)

domain assumption 2D hydrodynamical equations adequately represent planet-disk interactions for the purpose of ring formation
Invoked by the choice of simulation dimensionality in the abstract.

pith-pipeline@v0.9.1-grok · 5818 in / 1266 out tokens · 32967 ms · 2026-06-29T14:58:32.443602+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

3 extracted references · 1 canonical work pages

[1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...
[2]

write newline

" write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...
[3]

- [1] #1 = = ^ ^ ^ .\!\!^ d .\!\!^ h .\!\!^ m .\!\!^ s .\!\!^ @mss

thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

work page doi:10.5281/zenodo.831784 2021

[1] [1]

, " * write output.state after.block = add.period write newline

ENTRY address archivePrefix author booktitle chapter doi edition editor eprint howpublished institution journal key month number organization pages publisher school series title misctitle type volume year version url label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts ...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION format.url url empty "" new.block "" url * "" * if FUNCTION format.eprint eprint empty "" archivePrefix empty "" archivePrefix "arXiv" = new.block " " eprint * " " * new.block " " eprint * " " * if if if FUNCTION format.doi doi empty "" " " doi * " " * if FUNCTION format.pid doi empty eprint empty ur...

[3] [3]

- [1] #1 = = ^ ^ ^ .\!\!^ d .\!\!^ h .\!\!^ m .\!\!^ s .\!\!^ @mss

thebibliography [1] 20pt to REFERENCES 6pt =0pt -12pt 10pt plus 3pt =0pt =0pt =1pt plus 1pt =0pt =0pt -12pt =13pt plus 1pt =20pt =13pt plus 1pt \@M =10000 =-1.0em =0pt =0pt 0pt =0pt =1.0em @enumiv\@empty 10000 10000 `\.\@m \@noitemerr \@latex@warning Empty `thebibliography' environment \@ifnextchar \@reference \@latexerr Missing key on reference command E...

work page doi:10.5281/zenodo.831784 2021