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exoALMA. VI. Rotating under Pressure: Rotation curves, azimuthal velocity substructures, and pressure variations

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Rotation curves of 15 planet-forming disks show that over 75% of dust rings and 80% of dust gaps coincide with gas pressure maxima and minima, making pressure variations the likely dominant cause of the observed continuum substructures.

desk verdict A careful, transparent survey of rotation-curve perturbations in 15 disks; the headline co-location statistic is plausible but needs a clearer denominator and a null baseline before it can carry the 'dominant mechanism' conclusion. read the letter →

arxiv 2504.20036 v1 pith:M3WFWFNC submitted 2025-04-28 astro-ph.EP

Jochen Stadler , Myriam Benisty , Andrew J. Winter , Andrés F. Izquierdo , Cristiano Longarini , Maria Galloway-Sprietsma , Pietro Curone , Sean M. Andrews
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Jaehan Bae Stefano Facchini Giovanni Rosotti Richard Teague Marcelo Barraza-Alfaro Gianni Cataldi Nicolas Cuello Ian Czekala Daniele Fasano Mario Flock Misato Fukagawa Himanshi Garg Cassandra Hall Iain Hammond Thomas Hilder Jane Huang John D. Ilee Kazuhiro Kanagawa Geoffroy Lesur Giuseppe Lodato Ryan A. Loomis Francois Menard Ryuta Orihara Christophe Pinte Daniel J. Price Hsi-Wei Yen Gaylor Wafflard-Fernandez David J. Wilner Lisa Wölfer Tomohiro C. Yoshida Brianna Zawadzki
This is my paper · ORCID
classification astro-ph.EP
keywords protoplanetarydisksplanetformationrotationcurvesgaspressuregradientsdustringandgapmolecularlinekinematicsALMAobservationsdiskverticalstratification
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 uses ALMA observations of 15 planet-forming disks to test whether the rings and gaps seen in the dust are carved by variations in gas pressure. It measures how the gas rotation speed departs from the velocity expected from the star's gravity alone, and shows that in over 75% of dust rings the gas rotates more slowly just inside the ring and faster just outside it—the signature of a pressure maximum—while over 80% of dust gaps show the reverse pattern, the signature of a pressure minimum. The same rotation curves reveal that the hotter upper gas layer ($^{12}$CO) rotates more slowly than the cooler lower layer ($^{13}$CO), evidence that the disks are vertically stratified. From these curves the paper derives, for the first time from observations, the radial pressure gradient at the disk midplane, and finds it consistent with the dust substructure positions. If the interpretation is right, gas pressure bumps become the leading explanation for the rings and gaps seen in planet-forming disks.

What carries the argument

The load-bearing object is the azimuthally averaged deviation from Keplerian rotation, $\delta\upsilon_{\phi} = \upsilon_{\phi} - \upsilon_k$, extracted from molecular-line centroid velocity maps. In centrifugal balance the deviation is tied to the pressure gradient by $\partial\ln P/\partial\ln R \approx 2\upsilon_k^2/c_s^2\, \delta\upsilon_{\phi}/\upsilon_k$, so the paper reads off pressure maxima and minima from the sign of $\partial\delta\upsilon_{\phi}/\partial R$ at each dust feature rather than from absolute velocities. A toy model with an imposed Gaussian gap in the pressure calibrates this sign mapping. Supporting pieces are a vertical-structure integral that converts the pressure gradient at the CO emitting height into a midplane pressure gradient, and a projection study of a planet-driven spiral wave showing that radial-flow contamination can change the amplitude of $\delta\upsilon_{\phi}$ by up to 25% while preserving the sign pattern of its radial profile.

What would settle it

A decisive test is to fit the full three-dimensional velocity field—including radial and vertical motions—from the same CO cubes in a few disks and recompute the pressure extrema from the sign of the corrected radial velocity gradient; any dust ring or gap where the sign reverses under this correction would falsify the co-location claim. A more targeted version is to examine disks with known warps or cavity flows, such as J1604 and HD 143006, and check whether their apparent pressure bumps survive when the axisymmetric-rotation assumption is relaxed.

Watch

Extended reading notes

Core claim

The central claim is that most dust continuum rings and gaps in the sample are co-located with gas pressure maxima and minima, so that gas pressure variations are likely the dominant mechanism forming these substructures. The evidence is the sign of the radial derivative of the deviation from Keplerian rotation, $\delta\upsilon_{\phi}$: a pressure maximum makes the rotation speed decrease with radius, and a pressure minimum makes it increase. In $^{12}$CO, 16 of 21 continuum rings and 10 of 12 gaps show the expected sign, and in $^{13}$CO the counts are 14 of 17 rings and 8 of 10 gaps. Because the diagnostic uses only the sign of the velocity gradient, the inferred pressure extrema do not depend on the exact stellar mass. The paper also reports vertical thermal stratification across most of the sample, sub-Keplerian rotation in the outer disks, and midplane pressure derivative profiles for a subset of sources.

Load-bearing premise

The argument assumes the measured gas motion is almost entirely circular rotation, so that any remaining small-scale velocity variation can be attributed to a pressure gradient; if unresolved radial flows or warps flip the sign of the velocity gradient at a dust feature, the pressure extremum inferred there is an artifact.

Editorial extensions

If this is right

  • Most dust rings and gaps are not independent dust phenomena: they mark gas pressure maxima and minima, so models of ring and gap formation should reproduce pressure bumps at those radii.
  • The midplane pressure derivative is now measurable from rotation curves and temperature maps, allowing direct confrontation with predicted dust drift speeds and dust-trapping efficiencies.
  • Vertical stratification is a general property of these disks, so single-molecule rotation curves cannot be translated into stellar masses without correcting for pressure support at the emitting height.
  • Sub-Keplerian rotation in the outer disk speeds up the inward drift of pebbles, potentially replenishing the inner disk with dust from large radii.
  • Gas pressure substructures beyond the dust continuum imply that outer pressure bumps either trap dust inefficiently or are short-lived, sharpening the question of what sets the outer dust radius.

Reading between the lines

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

  • The sign-based diagnostic is robust to the 25% amplitude projection error the paper quantifies, but not to sign flips from unmodeled radial flows; if some of the substructures classed as 'not accessible' were counted as failures, the 75% and 80% rates would be lower.
  • The pressure substructures seen beyond the dust continuum predict that deep continuum imaging at those radii should find little or no trapped dust; a targeted search is a straightforward test of whether those bumps are leaky, short-lived, or dust-free.
  • Applying the same rotation-curve technique to multiple isotopologues at different heights can separate density-driven from temperature-driven pressure variations, potentially turning the co-location statistic into a diagnostic of the physical origin of each bump.
  • If the co-location rates hold across a larger sample, continuum ring catalogs alone would become statistical tracers of gas pressure maxima, letting population studies probe the frequency of pressure bumps without needing kinematic data.
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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 paper presents azimuthally averaged rotation curves and Keplerian-subtracted velocity deviations (δυϕ) for 15 protoplanetary disks from the exoALMA Large Program, measured in 12CO and 13CO J=3–2 emission. It reports vertical thermal stratification inferred from the differing rotation of the two CO isotopologues, ubiquitous small- and large-scale δυϕ substructures, and a co-location statistic between dust continuum rings/gaps and gas pressure maxima/minima identified from the sign of the radial derivative of δυϕ. The paper also derives midplane logarithmic pressure gradients for a subset of disks, discusses systematic uncertainties including beam smearing, projection effects, and stellar-mass offsets, provides rough planet-mass estimates for some gaps, and releases the extracted radial profiles as a Value-Added Data Product. The central claim is that more than 75% of dust rings and 80% of dust gaps are co-located with pressure maxima and minima, implying that gas pressure variations are the likely dominant mechanism for continuum substructure formation.

Significance. If the co-location claim holds, the paper would supply the strongest observational support to date for pressure-bump dust trapping as the leading explanation of ring and gap formation in protoplanetary disks, extending earlier smaller-sample results (e.g., Izquierdo et al. 2023) to a homogeneous ALMA Large Program sample. The paper's strengths include a careful and transparent velocity extraction with documented systematics, a sign-based diagnostic that is independent of the absolute stellar-mass offset, and a public release of the kinematic data products. The midplane pressure derivative derivations, though limited to a subset of sources, are a promising new observable. However, the headline co-location statistic is not yet on a sound statistical footing: its denominator is not fully defined, and no random-co-location baseline is established, so the significance of the percentages relative to a null hypothesis is currently unclear.

major comments (3)
  1. [Section 3.4 and Section 5.2] The co-location fraction reported in the abstract and Section 5.2 is computed on a sample that is partly defined by the outcome. Criterion (4) in Section 3.4 restricts entries in Table 1 to continuum substructures with a δυϕ gradient of the theoretically expected sign, and Section 5.2 explicitly states that substructures that could not be assessed are not included in the total count of non-aligning features. The reader cannot reconstruct the denominator of '16 out of 21 rings and 10 out of 12 gaps' from the text and tables alone. Please specify a fixed, pre-registered sample—all axisymmetric continuum rings and gaps with contrast ID/IB < 0.8 that are beam-resolved, including those with flat, reversed, or unassessable δυϕ gradients—and tabulate the co-location fraction over that full sample for each tracer separately.
  2. [Section 5.1 and Section 5.2] The headline statistic lacks a null expectation. The paper itself reports that δυϕ substructures are ubiquitous (Section 5.1), so a substantial fraction of continuum features would coincide with a local sign change of ∂δυϕ/∂R even if pressure bumps were unrelated to dust rings and gaps. To support the conclusion that gas pressure variations are 'likely the dominant mechanism' for ring and gap formation, provide a random-co-location baseline or permutation test, for example comparing the observed sign at continuum features with the distribution of signs at randomly drawn radii in the same disks.
  3. [Appendix D and Section 6.3] The sign-based diagnostic is robust to the stellar-mass offset because a constant offset shifts δυϕ vertically without changing the sign of its radial derivative, but the paper's assertion that 'the shape of the δυϕ-profile is hardly affected' by projection effects is only demonstrated for one planet-driven spiral simulation. Section 6.3 itself identifies beam smearing at steep intensity gradients, warps, and low-SNR outer-disk biases as sources of radial-dependent velocity errors that could, in principle, alter the sign of ∂δυϕ/∂R at some features. Because the co-location claim rests entirely on signs, please add tests that bound the fraction of sign flips under these systematics, for example using existing hydrodynamic simulations with radial or vertical flows, or by masking the innermost and outermost beams where biases are strongest, or temper the 'dominant mechanism' conclusion to the level of a consistency check.
minor comments (4)
  1. [Abstract and Section 5.2] The phrase 'resolved in δυϕ' should be defined explicitly; the current wording leaves open whether a continuum substructure is counted only when the δυϕ sign is measurable, which is precisely the selection effect at issue in the major comments.
  2. [Table 2 note] The note that unassessable substructures are 'not included in the total count of non-aligning δυϕ-substructures considered' should state how the total count of considered features is built and where that list is published, so that the denominator of the co-location fraction is transparent.
  3. [Section 6.2] The sentence 'Out of 17 continuum gaps with a positive CO δυϕ radial gradient' is hard to reconcile with the earlier counts (10 gaps for 12CO and 8 for 13CO); please clarify whether this is the sum over both tracers and over which gap sample, and align the numbering with Table 1 and Table 2.
  4. [Figure E.1 caption] The caption describes both the High Resolution Images and the High Surface Brightness Sensitivity Images as 'red'; one of the colors in the caption is presumably a typo.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the co-location statistic compares independent continuum and kinematic observables, and the reporting criteria do not force the claimed alignment fraction.

full rationale

The central claim is self-contained. Dust ring and gap locations come from an independent continuum catalog (Curone et al. 2024), while pressure maxima/minima are inferred from the sign of the radial derivative of the azimuthally averaged line-centroid velocity δυϕ. The paper explicitly avoids the stellar-mass degeneracy by using the derivative sign rather than δυϕ=0 crossings (Sec. 3.3: 'we circumvent this problem by investigating the sign of the radial derivative of δυϕ'). Non-aligning and unassessable continuum features are explicitly listed in Table 2, so the reported 16/21 rings and 10/12 gaps are not generated by the Section 3.4 reporting criterion (4), which only determines which aligning features receive width/amplitude measurements in Table 1. The numerous self-citations to discminer, emission-surface fits, temperature models, and kinematic stellar masses refer to public code and data products from the same program; they do not encode the target conclusion and are not the load-bearing premise of the co-location statistic. The lack of an explicit random-co-location baseline and the partially unspecified denominator are statistical-interpretation concerns, not circularity of the derivation.

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

The paper's derived quantities rest on fitted inputs from companion exoALMA papers (stellar masses, emission surfaces, temperature structures, continuum substructure catalog) and on physical assumptions of hydrostatic equilibrium, centrifugal balance, and negligible radial flows at the emission surface. The conservative sign-of-gradient method mitigates the stellar-mass degeneracy, but the midplane pressure derivative inherits the full covariance of the temperature and surface-height fits, which are not propagated.

free parameters (5)
  • Kinematic stellar mass M* (discminer fit) = Per-disk/per-line best-fit values from Izquierdo et al. 2024; not listed in text
    Fitted to line centroid velocity maps assuming pure Keplerian rotation; used to compute υk and δυϕ. Offsets of ~5% from the true mass shift δυϕ vertically, mitigated by using the sign of the radial gradient.
  • Midplane temperature power-law index qmid = Per-disk values; sample mean -0.32 used when unavailable
    Used in Eq. 11 and Eq. C13 to compute the isothermal height-difference baseline and the midplane pressure derivative. Inferred in companion paper Galloway-Sprietsma et al. 2024 from the same exoALMA data.
  • Emission surface parameters z0, pz, Rt, qt = Per-disk/per-line discminer surface fits (Izquierdo et al. 2024)
    Equation 8 gives the emitting height z(R) used in Eq. 7 for the Keplerian correction and in Appendix C for the midplane pressure derivative; derived from the same line data.
  • Stellar mass and self-gravity from Longarini et al. 2024 = Per-disk values from companion paper
    Used in Section 6.1 for the midplane pressure derivative and for self-gravity corrections in disks with Mdisk > 0.05 M_sun; fitted to the same CO rotation curves.
  • 2D temperature structure parameters (Tmid, Tatm, qmid, qatm, Z0, qz) = Per-disk posteriors from Galloway-Sprietsma et al. 2024
    Used in Eq. C14 to compute cs(R,z) and the vertical pressure integration in Eq. 12 and 13. These are fitted to the same ALMA data by the same team.
assumptions (5)
  • domain assumption The disk is in vertical hydrostatic equilibrium (Eq. C3, Appendix C)
    Used to derive the midplane pressure derivative in Section 6.1. If the emission layer is not in hydrostatic equilibrium, the inferred ∂lnPmid/∂lnR is not reliable.
  • domain assumption The azimuthally averaged line-of-sight velocity is dominated by axisymmetric azimuthal rotation; radial and vertical flows are negligible (Eq. 6)
    The rotation-curve extraction projects vlos into vphi assuming axisymmetry. Warps and radial flows can produce spurious delta_vphi (Section 6.3, Appendix D).
  • domain assumption Small-scale delta_vphi substructures are caused by local gas pressure gradients; self-gravity only contributes on large scales (Section 3.3)
    This justifies attributing the sign of d(delta_vphi)/dR to pressure maxima and minima. The paper later includes self-gravity for massive disks in Section 6.1.
  • standard math The Dartois et al. (2003) power-law plus cosine temperature parameterization describes the vertical thermal structure (Eq. C12-C14)
    Adopted from the literature and fitted by Galloway-Sprietsma et al. 2024; required for the vertical integration in Appendix C.
  • domain assumption The CO line centroid traces the local gas velocity without significant optical depth or excitation biases (implicit via discminer)
    The double-bell line fitting is described in Section 3.1; line-intensity gradients can shift the centroid within a beam (Section 6.3).

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Cite this review

Pith. "Pith review of exoALMA. VI. Rotating under Pressure: Rotation curves, azimuthal velocity substructures, and pressure variations." pith.science (2026). https://pith.science/paper/M3WFWFNC

@misc{pith2026250420036,
  author       = {Pith},
  title        = {Pith review of: exoALMA. VI. Rotating under Pressure: Rotation curves, azimuthal velocity substructures, and pressure variations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/M3WFWFNC}},
  note         = {Machine review of arXiv:2504.20036}
}
abstract

The bulk motion of the gas in protoplanetary disks around newborn stars is nearly Keplerian. By leveraging the high angular and spectral resolution of ALMA, we can detect small-scale velocity perturbations in molecular line observations caused by local gas pressure variations in the disk, possibly induced by embedded protoplanets. This paper presents the azimuthally averaged rotational velocity and its deviations from Keplerian rotation ($\delta\upsilon_{\phi}$) for the exoALMA sample, as measured in the $^{12}$CO and $^{13}$CO emission lines. The rotation signatures show evidence for vertically stratified disks, in which $^{13}$CO rotates faster than $^{12}$CO due to a distinct thermal gas pressure gradient at their emitting heights. We find $\delta\upsilon_{\phi}$-substructures in the sample on both small ($\sim$10 au) and large ($\sim$100 au) radial scales, reaching deviations up to 15% from background Keplerian velocity in the most extreme cases. More than 75% of the rings and 80% of the gaps in the dust continuum emission resolved in $\delta\upsilon_{\phi}$ are co-located with gas pressure maxima and minima, respectively. Additionally, gas pressure substructures are observed far beyond the dust continuum emission. For the first time, we determined the gas pressure derivative at the midplane from observations and found it to align well with the dust substructures within the given uncertainties. Based on our findings, we conclude that gas pressure variations are likely the dominant mechanism for ring and gap formation in the dust continuum.

Figures

Figures reproduced from arXiv: 2504.20036 by the authors.

Figure 1
Figure 1. (a) Azimuthal velocities (left axis, black lines) and midplane pressure (right axis, blue lines), (b) along with the deviations from Keplerian rotation and the first radial derivative of the pressure, for a hydrodynamic model with an imposed Gaussian gap in the pressure at R = 240 au. The pressure minimum and maximum locations are marked with vertical purple dashed and full lines, respectively. The circles in (b) ma… view at source ↗
Figure 2
Figure 2. Rotation curves υϕ(R, z(R)) measured from 12CO (red) and 13CO (blue), shown of all sources using the High Surface Brightness Sensitivity Images. For radii smaller than twice the beam size, the curves are plotted with dashed lines due to uncertainties in the velocity extraction. The colored shaded area of the lines shows the standard deviation within each extracted radial annulus usually on the order of ≈ 10 − 50 m/s… view at source ↗
Figure 3
Figure 3. Level of vertical stratification between 12CO and 13CO rotation curves outside of two beam sizes from the center. The turquoise line displays the expected isothermal velocity shift solely due to the differences in emitting height (RHS Eq. 11). radius. For a power-law density profile, this would intro￾duce only a minor deviation of about 1-2 % υk (Rosen￾feld et al. 2013; Andrews et al. 2024). However, if the density … view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Radial profiles of δυϕ for 12CO J = 3 − 2 of all sources focused on the region beyond the continuum substructures using the High Surface Brightness Sensitivity Images. The error bars show the standard deviation within each extracted radial annulus. The vertical dashed-…
Figure 5
Figure 5. Figure 5: Radial profiles of δυϕ for 12CO J = 3 − 2 of all sources focused on the region of the continuum substructures, using the High Resolution Images. The profiles are plotted starting at two beam sizes from the disk center and the error bars show the standard deviation of e…
Figure 6
Figure 6. Figure 6: 12CO δυϕ profiles for selected sources focused on the region of the continuum emission with highlighted radial locations of pressure substructures (red vertical lines). From [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: Radial profiles of ∂lnPmid/∂lnR for selected sources, focused on the region of their continuum substruc￾tures. The vertical colored arrows in the upper left show variations in the stellar mass of ±3 % which would result in a shift of the whole profiles up and down. We …

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.