exoALMA. VI. Rotating under Pressure: Rotation Curves, Azimuthal Velocity Substructures, and Gas Pressure Variations

This paper asks whether small-scale deviations from Keplerian rotation in protoplanetary disks—measured with ALMA at high angular and spectral resolution—can be used to infer gas pressure substructures, and whether those pressure variations are spatially correlated with the dust rings and gaps seen in the millimeter continuum. The question matters because dust substructures are widely interpreted as signatures of planet formation and disk dynamics, but the physical origin of rings and gaps (e.g., embedded planets carving gas gaps, versus alternative mechanisms like ice lines, zonal flows, or dust-only processes) remains difficult to disentangle. Gas kinematics provide a more direct dynamical tracer: in centrifugal balance, the radial pressure gradient perturbs the orbital speed, so localized pressure maxima and minima should imprint themselves as systematic patterns in the azimuthal velocity residuals.

The authors analyze the exoALMA sample (15 disks) using CO lines: specifically the 12CO and 13CO full emission-line data cubes (they omit CS for most disks because reliable azimuthal velocities are difficult to extract). The study design is observational and comparative across a heterogeneous set of disks. For each disk and tracer, they extract azimuthally averaged rotation curves and compute deviations from Keplerian rotation, denoted $\delta v_{\varphi }$. They also use the emission-layer heights inferred from disc modeling to interpret vertical stratification: because 12CO and 13CO originate at different altitudes, differences in their rotation curves can reveal differences in the thermal pressure gradient with height.

Methodologically, the paper combines (i) line centroid extraction with (ii) geometric deprojection and (iii) a pressure-kinematics mapping. For centroid velocities, they use discminer to fit a Keplerian disk model to the line profile in each channel, explicitly modeling both the front and back surfaces—important for moderately to highly inclined disks where line profiles can be double-peaked. For rotational velocity, they decompose the line-of-sight velocity into cylindrical components and then infer $v_{\varphi }$ by azimuthal averaging of the centroid map after subtracting the systemic velocity, masking regions near the minor axis where deprojection becomes unstable. They compute the Keplerian reference speed using a kinematic stellar mass parameter from discminer fits; they caution that these are not “true” stellar masses because discminer assumes a purely Keplerian model and does not explicitly include pressure and self-gravity terms. They estimate that the kinematic stellar masses can differ from true stellar masses by about $\sim 5\%$, which mainly introduces a constant offset in $\delta v_{\varphi }$ rather than strongly changing its radial shape.

To connect $\delta v_{\varphi }$ to pressure, they neglect the disk self-gravity term for the initial pressure-gradient inference (arguing it is subdominant to pressure in their regime), and derive an approximate relation between the logarithmic pressure gradient at the emission height and the observed velocity residuals. They then use the sign of the radial derivative of $\delta v_{\varphi }$ (i.e., whether $\delta v_{\varphi }$ increases or decreases with radius) as a diagnostic for whether the underlying pressure is at a maximum or minimum. They further restrict quantitative substructure measurements to cases where dust rings/gaps are axisymmetric, well resolved, and meet contrast and width criteria.

The key findings are threefold. First, the CO rotation curves show evidence for vertical thermal stratification: in most disks, the 13CO-emitting layer rotates faster than the 12CO layer, and the mismatch is larger than can be explained by gravity alone under an isothermal assumption. This implies that the thermal pressure gradient differs with height, consistent with a hot surface layer and a cooler midplane. Second, azimuthal velocity residual substructures are ubiquitous across the sample on both small and large radial scales. The paper reports deviations from Keplerian rotation reaching up to about 15% in the most extreme cases, and it identifies $\delta v_{\varphi }$-substructures on scales of roughly $\sim 10$ au and $\sim 100$ au.

Third—and most important for the dust-structure origin—the authors find strong spatial co-location between dust continuum rings/gaps and gas pressure extrema inferred from kinematics. Using the sign of the radial derivative of $\delta v_{\varphi }$ (at the CO emission height), they find that for 12CO, 16 out of 21 continuum rings align with the expected pressure-maximum/minimum behavior (reported as negative $\mathrm{d}\delta v_{\varphi }/\mathrm{d}R$ for rings and positive for gaps), and 10 out of 12 continuum gaps align accordingly. For 13CO, 14 out of 17 rings and 8 out of 10 gaps show the expected alignment. Taken together, this corresponds to “more than 75%” of rings and “80%” of gaps co-located with gas pressure maxima and minima, respectively. The authors emphasize that these kinematic signatures appear in the line centroids (velocity structure) rather than in line intensities.

They also report that pressure substructures extend beyond the dust continuum emission, suggesting that gas pressure variations are not always efficiently trapping millimeter dust at large radii. For the first time in this series, they infer the midplane pressure derivative directly from observations for a subset of disks by combining emission heights, a 2D temperature structure, and a self-consistent vertical pressure mapping. In selected cases (e.g., J1615, LkCa 15, V4046 Sgr), the inferred midplane pressure derivative $\partial \ln P/\partial \ln R$ aligns with the locations of dust substructures within uncertainties.

The paper acknowledges several limitations and potential systematics. The dominant uncertainty in pressure-gradient inference comes from the stellar mass used to set the Keplerian background; even a few percent uncertainty in $M_{\star }$ can dominate the error budget, though it largely shifts $\delta v_{\varphi }$ by a constant. They also discuss biases from velocity extraction: intensity gradients within a beam can shift the measured centroid, potentially producing artificial sub- or super-Keplerian signals, especially in the inner disk where angular resolution is limited. They address projection-related misinterpretation between radial and azimuthal velocity components in the presence of non-axisymmetric perturbations (e.g., planet-driven spirals), using a hydrodynamical parameter study; they conclude that while the amplitude of $\delta v_{\varphi }$ can change with planet azimuth, the radial location of inferred pressure gaps remains robust. Finally, they note that some rings do not show clear pressure alignment, which could reflect measurement limitations near the inner edge, or alternative ring-formation mechanisms (ice lines, transient zonal flows, dust traffic jams, or dust back-reaction).

In practical terms, the results imply that high-resolution molecular kinematics can be used as a diagnostic of gas pressure structure and therefore of the dynamical processes shaping dust rings and gaps. Observers and modelers should care because the study provides a quantitative, sample-wide empirical link between gas pressure extrema and dust substructures, supporting pressure variations as a dominant mechanism for ring/gap formation. This has implications for interpreting ALMA continuum images: rings and gaps are not merely morphological features but likely trace underlying pressure traps and density gaps, potentially associated with embedded planets or other pressure-generating instabilities. The authors also release the derived rotation curves, residuals, and midplane pressure derivatives as a public value-added data product, enabling follow-up analyses and cross-comparisons with planet-detection claims and disk-evolution models.