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exoALMA XII: Weighing and sizing exoALMA disks with rotation curve modelling

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

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Pith's one-line read A measurable self-gravity signal in CO rotation curves weighs the gas in ten protoplanetary disks and finds most are at least 5% of their star's mass.

desk verdict Convincing new dynamical disk masses for ten exoALMA disks, though the fixed surface-density slope (γ=1) and unpublished companion papers leave the error budget less airtight than the headline numbers suggest. read the letter →

arxiv 2504.18726 v1 pith:REY3UYR3 submitted 2025-04-25 astro-ph.EP astro-ph.IM

Cristiano Longarini , Giuseppe Lodato , Giovanni Rosotti , Sean Andrews , Andrew Winter , Jochen Stadler , Andrés Izquierdo , Maria Galloway-Spriestma
show 33 more authors
Stefano Facchini Pietro Curone Myriam Benisty Richard Teague Jaehan Bae Marcelo Barraza-Alfaro Gianni Cataldi Ian Czekala Nicolás Cuello Daniele Fasano Mario Flock Misato Fukakgwa Himanshi Garg Cassandra Hall Iain Hammond Caitlyn Hardiman Thomas Hilder Jane Huang John Ilee Andrea Isella Kazuhiro Kanagawa Geoffroy Lesur Ryan A. Loomis François Ménard Ryuta Orihara Christophe Pinte Daniel J. Price Leonardo Testi Gaylor Wafflard-Fernandez Lisa Wölfer Hsi-Wei Yen Tomohiro C. Yoshida Brianna Zawadzki
This is my paper · ORCID
classification astro-ph.EPastro-ph.IM
keywords protoplanetarydisksrotationcurvesdynamicaldiskmassesself-gravitypressuregradientgas-to-dustratioviscousevolutionexoALMA
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

The paper tries to show that the small departures of a protoplanetary disk's rotation curve from pure Keplerian motion carry enough information to weigh the disk and pin down its scale radius. It models the $^{12}$CO and $^{13}$CO rotation curves of ten disks from the exoALMA sample with a vertically stratified disk model that includes both the pressure gradient and the disk's self-gravity, obtaining dynamical disk masses for all ten. Seven sources land above the $M_d/M_\star = 0.05$ threshold where the method is reliable. The resulting masses imply an average gas-to-dust ratio of roughly 400 rather than the standard 100, and effective viscosity parameters $\alpha_S$ spanning $10^{-5}$ to $10^{-2}$.

What carries the argument

The central object is the rotation-curve model for a vertically stratified disk, which decomposes $v_\phi^2$ into the stellar Keplerian term, a finite-height correction, the pressure-gradient term, and a self-gravity integral $v_d^2$ (Eq. A13). The disk surface density is assumed to follow the self-similar Lynden-Bell & Pringle profile with power-law index fixed at $\gamma=1$, and the two-dimensional temperature structure follows the Dartois prescription with parameters fixed from companion thermal fits to the same sources. The fitting code varies stellar mass, disk mass, and scale radius simultaneously against the $^{12}$CO and $^{13}$CO rotation curves, propagating thermal-structure uncertainties by repeating each fit 100 times.

What would settle it

Measure gas masses for the same ten disks with a tracer that avoids CO chemistry and dust optical-depth assumptions, such as hydrogen deuteride (HD) emission or N2H+ emission. If these independent masses cluster near the dust-based masses with gas-to-dust near 100, rather than matching the dynamical masses, the self-gravity interpretation of the rotation curves would be refuted.

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Extended reading notes

Core claim

The paper's central claim is that the self-gravitating contribution to the gravitational potential is directly measurable in CO rotation curves, so dynamical disk masses can be derived without assuming anything about chemistry or dust opacity. For the ten exoALMA disks analyzed, the best-fit disk masses range from about $0.04\,M_\odot$ to $0.16\,M_\odot$, with seven disks above the $5\%$ disk-to-star mass detection threshold. Combined with the fitted scale radii, these masses show all of the disks to be gravitationally stable (Toomre $Q>1$), imply an averaged gas-to-dust ratio near 400 under the optically thin dust assumption, and, together with accretion rates, give effective $\alpha_S$ values between $10^{-5}$ and $10^{-2}$.

Load-bearing premise

The surface-density profile is assumed to be smooth and self-similar with its power-law index fixed at $\gamma=1$, and if the true profile differs, the pressure-gradient and self-gravity contributions shift, biasing the derived scale radius and, to a lesser extent, the masses.

Editorial extensions

If this is right

  • Seven of the ten exoALMA disks have $M_d/M_\star > 0.05$, so the sample now provides robust dynamical disk masses that straddle the method's detection threshold.
  • All disks in the sample are gravitationally stable with Toomre $Q>1$, consistent with the absence of prominent spiral structure in these systems.
  • The average gas-to-dust ratio near 400, combined with optically thin dust masses, implies that either dust masses are systematically underestimated or the disks genuinely have elevated gas-to-dust ratios.
  • The effective $\alpha_S$ values span four orders of magnitude, from $10^{-5}$ to $10^{-2}$, indicating that a single viscosity parameter does not describe angular-momentum transport across the sample.
  • The comparison of dynamical scale radii with flux-based radii suggests that substructures slow radial drift of dust and that CO depletion can reconcile observed CO radii with thermochemical model predictions.

Reading between the lines

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

  • If the low-$\alpha_S$ end of the inferred range is real, those disks cannot be transporting angular momentum primarily through turbulence, making non-turbulent mechanisms such as magnetically launched winds a more natural explanation; the paper does not draw this conclusion.
  • A testable extension would be to check whether the fitted scale radius $R_c$ coincides with the outermost dust substructure in each disk, which would directly test the claim that pressure-modulated substructures are responsible for the small dust radii.
  • If the gas-to-dust ratio near 400 is due to optically thick dust rather than genuinely high gas content, modeling the continuum with optical-depth effects at multiple wavelengths should raise the estimated dust masses and bring the ratio closer to 100.
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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. This paper models the azimuthally averaged rotation curves of 12CO and 13CO for ten exoALMA disks using the vertically stratified model of Lodato et al. (2023) and Martire et al. (2024), fitting the stellar mass, disk mass, and scale radius from the combined pressure-gradient and self-gravity signatures. The surface density is assumed to follow the Lynden-Bell & Pringle self-similar form with the power-law index fixed to gamma=1. From the fitted parameters the paper derives disk-to-star mass ratios, Toomre Q profiles, gas-to-dust ratios using the continuum dust masses of Curone et al. (2025), flux-radius comparisons, and effective alpha_S values. AA Tau is excluded from the statistical analysis because of diffuse-backside contamination. Seven of the ten sources are claimed to have Md/M* above the 5% detection threshold, and the dynamical masses for DM Tau, HD 34282, and LkCa15 are compared with independent literature estimates.

Significance. If the derived masses are robust, this is a valuable dynamical census: the method is chemistry-free, the sample is well characterized, the DySc code is public, and the propagation of thermal-structure systematics through 100 posterior draws is a clear improvement over earlier work. The few-percent agreement of the dynamical stellar masses with discminer results and the consistency with independent disk-mass estimates for three sources provide genuine supporting evidence. However, the headline quantitative claims, including the average gas-to-dust ratio of about 400 and the number of secure disk-mass detections, currently rest on an assumed surface-density shape and on fiducial masses for systems below the detection threshold, so the conclusions are important but conditional.

major comments (3)
  1. [Appendix B / Eq. (A13)] The robustness of the disk masses to the assumed surface-density slope gamma is asserted but not demonstrated in this paper. The text fixes gamma=1 and states that this choice "underestimates the true uncertainties" and "introduces a potential bias on the scale radius", referring to Andrews et al. (2024) for the claim that the disk and stellar masses are unaffected. Since the pressure-gradient term in Eq. (A13) contains gamma both through gamma' and through (2-gamma)(R/Rc)^(2-gamma), changing gamma changes the radial profile of the non-Keplerian correction, and the three fitted parameters (M*, Md, Rc) can partially absorb that change. With the detection classification set at Md/M*>0.05 and with J1615, J1842, and SY Cha at 0.07-0.10 with 15-30% errors, an unquantified systematic of this size is load-bearing. Please add gamma as a free parameter, or at minimum run the full sample with gamma=0.5 and gamma=1.5 and show the resulting distributions of Md and Rc.
  2. [Section 4.2.1 / Table 1] The average gas-to-dust ratio of about 400 is computed using the fiducial best-fit disk masses for all sources except AA Tau, including the three sub-threshold systems J1852, PDS66, and V4046 Sgr, for which Section 4.2 states that Md=0.05M* may be used as an upper limit instead. The individual gas-to-dust values for these systems carry uncertainties of order 100%, for example 364+342/-357 for PDS66. The average should be recomputed for the secure detections alone, and the effect of treating the three sub-threshold masses as upper limits should be reported; otherwise the "approximately 400" claim in the abstract is not supported by the data.
  3. [Section 2.2 / Section 3.2] The substructure test is performed on only one disk, LkCa15, even though the sample is dominated by disks that show pressure-modulated substructures and the quoted 50-70 m/s perturbations are comparable in magnitude to the non-Keplerian signals being fitted. To support the statement that substructures do not bias the dynamical masses across the sample, add a similar test for at least one additional source with prominent substructure, or show that the LkCa15 result is representative by comparing the residual amplitudes across the sample.
minor comments (4)
  1. [Appendix B / Table 5] The thermal-structure systematic is propagated from the Galloway-Sprietsma et al. (2025) posteriors, but Table 5 lists only the best-fit Dartois parameters without posterior widths; adding the widths would make the systematic treatment reproducible.
  2. [Section 4.2] The sentence "We are able to parametrically describe their surface density" overstates the result, since gamma is fixed to 1 and only a normalization (Md) and a scale (Rc) are fitted; the fitted family is a one-parameter subset of the self-similar solutions.
  3. [Section 4.3.1] The CO-depletion check based on Rosotti et al. (2025) is acknowledged to be non-independent of the dynamical masses; the text should present the Trapman et al. (2025) inference as the primary independent test in the main message rather than giving both equal weight.
  4. [Section 4.4] The assumption that the stellar accretion rate equals the disk accretion rate at Rc is noted in the text but not propagated into the alpha_S uncertainties; since the accretion-rate uncertainty of 0.35 dex dominates the error budget, a sentence quantifying this limitation in Table 3 or the figure caption would help.

Circularity Check

1 steps flagged · score 4.0 of 10

Central disk-mass results come from genuine fits with external benchmarks; the only load-bearing self-citation is the gamma=1 robustness claim deferred to an overlapping-author preprint.

  1. self citation load bearing [Appendix B (DySC code and statistical framework); cf. Eq. (A13) and Table 1]
    "All the fits are performed fixing the power law coefficient of the surface density γ = 1, underestimating the true uncertainties. In addition, this choice introduces a potential bias on the scale radius, that is the parameter most affected by the choice of γ, while the disk and stellar masses are not (Andrews et al. 2024)."

    The claim that fixing γ=1 leaves the disk and stellar masses unbiased is load-bearing for the central mass measurements and for the Md/M⋆>5% classification, but it is not demonstrated in this paper. It is deferred to Andrews et al. (2024), an arXiv preprint whose authors overlap with the present paper (Andrews, Teague, and Huang are co-authors). Since the pressure term in Eq. (A13) depends on γ through γ′ and (R/Rc)^(2−γ), and both pressure and self-gravity contribute to the small non-Keplerian residual, the robustness of Md and M⋆ to the assumed surface-density slope is not an independent mathematical fact here but an imported conclusion from a self-citation.

full rationale

The dynamical mass measurement itself is not circular: the free parameters M⋆, Md, and Rc are fit to observed 12CO and 13CO rotation curves through Eq. (A13), with Md entering through the self-gravity integral v_d^2 and the pressure term determined by the temperature structure. The derived gas-to-dust ratios (Md/Mdust, with Mdust from Curone et al. 2025), Toomre Q values (Eq. 8), and effective αS values (Eq. 10, with accretion rates from the literature) are external algebraic relations applied to fitted values, not quantities re-fit to reproduce themselves. The mass results are benchmarked against independent estimates: DM Tau against Trapman et al. (2022) and McClure et al. (2016), HD 34282 against Stapper et al. (2024), and LkCa15 against Jin et al. (2019); the αS values are also compared with independent line-broadening measurements. The Rosotti et al. (2025) CO-depletion comparison is explicitly disclosed as non-independent because it uses the dynamical masses from this paper, and the paper's CO-depletion discussion primarily relies on the independent Trapman et al. (2025) estimates, so that is not a circular step. The one load-bearing self-citation is the Appendix B assertion that fixing γ=1 does not bias Md and M⋆, which is deferred to an overlapping-author preprint rather than demonstrated here; this affects the systematic robustness of the headline disk-mass and 5% classification claims, but it does not make the fitted masses circular by construction. Overall, the central claims rest on independent fits and external benchmarks, with one load-bearing self-citation for the γ-systematics.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central measurements rest on a physical model with several domain assumptions inherited from the literature; the only hand-set parameter is gamma=1. No new physical entities are introduced.

free parameters (4)
  • Stellar mass M* = 0.468 to 1.777 M_sun per source (Table 1)
    Fitted to the rotation curves; a primary output.
  • Disk mass Md = 0.038 to 0.155 M_sun per source (Table 1)
    Fitted through the self-gravity term; the headline result.
  • Scale radius Rc = 28 to 370 au per source (Table 1)
    Fitted through pressure gradient and self-gravity; used in radius and alpha_S analyses.
  • Surface density power-law index gamma = 1 (fixed)
    Set by hand and not fit; the paper notes it underestimates uncertainties and biases Rc.
assumptions (6)
  • domain assumption Self-similar surface density profile (Lynden-Bell & Pringle 1974), Eq. (3)
    Assumed surface density shape; determines pressure gradient and self-gravity contributions.
  • domain assumption Centrifugal balance and axisymmetry of the rotation curve (Eq. A12)
    The model assumes the radial momentum equation is dominated by gravity, pressure, and centrifugal terms; non-axisymmetric sources are excluded.
  • domain assumption Dartois 2D temperature prescription with parameters from Galloway-Sprietsma et al. (2025)
    Temperature structure enters the pressure gradient term; parameters are taken from a companion paper.
  • domain assumption Optically thin dust continuum emission for dust masses (Curone et al. 2025)
    Used to derive gas-to-dust ratios; the paper notes this underestimates dust mass.
  • domain assumption Self-similar viscous evolution to relate accretion rate to alpha_S (Eq. 10)
    Assumes the disk accretes self-similarly and that stellar accretion rate equals disk accretion at Rc.
  • standard math Standard equations of hydrostatic equilibrium and gravitation (Appendix A)
    The rotation curve derivation uses Navier-Stokes, Poisson equation, and complete elliptic integrals.

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Cite this review

Pith. "Pith review of exoALMA XII: Weighing and sizing exoALMA disks with rotation curve modelling." pith.science (2026). https://pith.science/paper/REY3UYR3

@misc{pith2026250418726,
  author       = {Pith},
  title        = {Pith review of: exoALMA XII: Weighing and sizing exoALMA disks with rotation curve modelling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/REY3UYR3}},
  note         = {Machine review of arXiv:2504.18726}
}
abstract

The exoALMA large program offers a unique opportunity to investigate the fundamental properties of protoplanetary disks, such as their masses and sizes, providing important insights in the mechanism responsible for the transport of angular momentum. In this work, we model the rotation curves of CO isotopologues $^{12}$CO and $^{13}$CO of ten sources within the exoALMA sample, and we constrain the stellar mass, the disk mass and the density scale radius through precise characterization of the pressure gradient and disk self gravity. We obtain dynamical disk masses for our sample measuring the self-gravitating contribution to the gravitational potential. We are able to parametrically describe their surface density, and all of them appear gravitationally stable. By combining dynamical disk masses with dust continuum emission data, we determine an averaged gas-to-dust ratio of approximately 400, not statistically consistent with the standard value of 100, assuming optically thin dust emission. In addition, the measurement of the dynamical scale radius allows for direct comparison with flux-based radii of gas and dust. This comparison suggests that substructures may influence the size of the dust disk, and that CO depletion might reconcile our measurements with thermochemical models. Finally, with the stellar mass, disk mass, scale radius, and accretion rate, and assuming self-similar evolution of the surface density, we constrain the effective $\alpha_S$ for these systems. We find a broad range of $\alpha_S$ values ranging between $10^{-5}$ and $10^{-2}$.

Figures

Figures reproduced from arXiv: 2504.18726 by the authors.

Figure 1
Figure 1. Top panels: rotation curves of LkCa15 (red dots) with the best fit model (blue lines) and residuals according to Eq. (A13). The black dashed line represents the location of the scale radius Rc. Bottom panel: Non-Keplerian contribution to the rotation curve, where δvz is the correction due to the finite height of the emission, δvp is the pressure gradient and δvd is the self-gravitating contribution. Galloway-Spriets… view at source ↗
Figure 2
Figure 2. Comparison between dynamical disk masses (this work) and literature estimates. Curone et al. (2025) underestimate the total dust mass, because of the optically thin emission hypothesis. In￾deed, we expect the sources within the sample to be, at least, marginally optically thick in the inner parts. In addition, Stapper et al. (2024) estimated gas masses of Herbig disks, and compared them with dust masses to obtain th… view at source ↗
Figure 3
Figure 3. Dynamical masses against dust masses as com￾puted in Curone et al. (2025) for the exoALMA and MAPS sources. The black line shows the Mdyn = 100Mdust and the brown line the Mdyn = 400Mdust. itationally stable. We underline that the temperature at the midplane is extrapolated from the 2D thermal structures (Galloway-Sprietsma et al. 2025). 4.3. Scale radii In this section we discuss the relationship between the flux b… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Top panel: Surface density and Toomre Q profiles for the four most massive disks of our sample, namely DM Tau, HD 34282, LkCa 15 and SY Cha, excluding AA Tau because of the big uncertainties (see Appendix E). Bottom panel: Surface density and Toomre Q profiles for the …
Figure 5
Figure 5. Figure 5: Flux based radii (i.e. radii enclosing the 68% of the emission) of 12CO, 13CO and dust compared with the dynamical scale radii Rc. The orange squares are the exoALMA sources, while the blue ones are the MAPS. The black line shows when the flux radius is equal to the dy…
Figure 6
Figure 6. Figure 6: Comparison between the observed and the pre￾dicted radius enclosing the 90% of the 12CO emission, ac￾cording to Eq. (9). The grey crosses show the results assum￾ing the CO depletion obtained by Trapman et al. (2025). αS, i.e. the amount of transported angular momentum.…
Figure 7
Figure 7. Figure 7: αS for the exoALMA and MAPS sources, com￾puted according to Eq. 10 and comparison with literature values. detailed values along with their associated uncertainties. The determination of αS involves two primary sources of error: the uncertainties related to the accretio…
Figure 8
Figure 8. Figure 8: Rotation curve of the disks within our sample (red dots) of the 12CO (left panels) and 13CO (right panels) with the best fit model using Eq. (A13) [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: Rotation curve of the disks within our sample (red dots) of the 12CO (left panels) and 13CO (right panels) with the best fit model using Eq. (A13) [PITH_FULL_IMAGE:figures/full_fig_p017_9.png]
Figure 10
Figure 10. Figure 10: Rotation curve of the disks within our sample (red dots) of the 12CO (left panels) and 13CO (right panels) with the best fit model using Eq. (A13) [PITH_FULL_IMAGE:figures/full_fig_p018_10.png]
Figure 11
Figure 11. Figure 11: Corner plots for AA Tau, DM Tau, Hd34282 and J1615. Andrews, S. M., Wilner, D. J., Hughes, A. M., Qi, C., & Dullemond, C. P. 2009, ApJ, 700, 1502, doi: 10.1088/0004-637X/700/2/1502 —. 2010, ApJ, 723, 1241, doi: 10.1088/0004-637X/723/2/1241 Ansdell, M., Williams, J. P.…
Figure 12
Figure 12. Figure 12: Corner plots for J1842, J1852, LkCa15 and PDS66. Fairlamb, J. R., Oudmaijer, R. D., Mendigut´ıa, I., Ilee, J. D., & van den Ancker, M. E. 2015, MNRAS, 453, 976, doi: 10.1093/mnras/stv1576 Flaherty, K., Hughes, A. M., Simon, J. B., et al. 2020, ApJ, 895, 109, doi: 10.3…
Figure 13
Figure 13. Figure 13: Corner plots for SY Cha and V4046 Sgr. Izquierdo, A. F., Stadler, J., Bae, J., et al. 2025, ApJL, TBD Izquierdo, A. F., Testi, L., Facchini, S., Rosotti, G. P., & van Dishoeck, E. F. 2021, A&A Izquierdo, A. F., Testi, L., Facchini, S., et al. 2023, A&A, 674, A113, doi…
Figure 14
Figure 14. Figure 14: Top panel: Surface density and Toomre Q profiles of AA Tau, where the errorbar is computed by propagating the uncertainties on star and disk masses. Bottom panel: Rotation curve of AA Tau compared to a Keplerian curve (top panel) and comparison between the non-paramet…

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Forward citations

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Pith tools

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