exoALMA. III. Line-intensity Modeling and System Property Extraction from Protoplanetary Disks

This paper addresses a practical but scientifically central question in protoplanetary disk spectroscopy: how can we reliably extract the physical and dynamical structure of inclined gas disks from ALMA molecular line cubes when the observed emission is a superposition of contributions from the disk’s front and back sides along each line of sight? This matters because velocity and intensity “substructures” (e.g., kinks and wiggles in channel maps) are among the main observational handles for planet–disk interactions, yet they can be mimicked or distorted by projection effects, finite angular resolution, and tracer-dependent optical depth. If the analysis pipeline incorrectly attributes front/back overlap, then inferred quantities such as stellar mass, inclination, systemic velocity, and rotation profiles can be biased, and apparent gas substructures may be misinterpreted.

The authors present a methodology within the exoALMA large program to model and analyze 12CO, 13CO, and CS line emission in 15 circumstellar disks. The core contribution is an improved line-intensity modeling and line-profile extraction workflow built on the discminer framework. For optically thin tracers (notably CS and, in some cases, 13CO), they introduce a composite “line profile kernel” approach that accounts for increased intensities caused by projected overlap between the front and back sides of the disk. For optically thick tracers (12CO and generally 13CO), they retain a front/back treatment that selects the higher-intensity component per pixel and velocity channel, following earlier discminer methodology.

Methodologically, the study uses ALMA continuum-subtracted fiducial image cubes for 12CO and 13CO J = 3–2 and CS J = 7–6, with a synthesized beam of 0.′′15 for the fiducial datasets and 0.′′3 for the higher-surface-brightness LkCa 15 analysis. Channel spacings are 100 m s−1 for 12CO and 13CO and 200 m s−1 for CS. The modeling stage generates Keplerian channel maps using discminer with a parametric intensity field that decreases with radius (with a broken power-law option near the center) and a Keplerian velocity field that depends on stellar mass and emission height. The emission surfaces are represented as geometrically narrow upper and lower layers with heights parameterized by a normalization and power-law indices (z0, p, Rt, q). The model intensity in each velocity channel is computed using a “bell” kernel rather than a Gaussian, motivated by the flat-topped and rapidly decaying line shapes typical of optically thick emission; the bell kernel includes a line-slope parameter that allows it to approximate a Gaussian in the optically thin limit.

A key modeling detail is how front and back sides are combined. For optically thick emission, the pipeline uses a “mask” strategy: at each pixel and velocity channel, it takes the higher-intensity of the two sides, so the dominant component controls the profile. For optically thin emission, it uses a “sum” strategy: it adds the front and back contributions directly to form the total line profile. This distinction is central to correctly reproducing moment maps and radial profiles in inclined disks. The authors also note that if optically thin emission is not confined to a geometrically narrow region, retrieved line widths and centroids can be biased by line-of-sight layering; however, they argue that for CS the likely emission thickness is smaller than 50 au, and prior work suggests centroid/width discrepancies remain below 30 m s−1 even for relatively thick slabs.

Parameter inference is performed with MCMC using emcee, maximizing a Gaussian log-likelihood in the image plane. Flat priors are used, with at least 10 walkers per free parameter, and the chains are run for about 20,000 iterations; best-fit parameters are taken as the median of the last 10% of iterations. The paper reports that formal uncertainties from this simplified noise model are typically around 0.1% for stellar mass and inclination and around 0.5% for the upper-surface height normalization, but they emphasize that spatially correlated noise can inflate uncertainties by about a factor of 10 for velocity, orientation, and surface parameters (citing Hilder et al. 2025).

The paper then introduces an analysis stage for extracting moment maps and radial profiles from line-profile observables. Because inclined disks often show double-peaked spectra due to emission from elevated surfaces, the authors implement a guided, iterative two-component fitting method. For low-inclination, single-peaked sources (inclination < 40°), they default to single-component fits (Gaussian or bell) to derive moment maps. For mid- and high-inclination sources ( i > 40°), they default to double-bell fits that decompose the profile into a primary component (associated with the front side) and a secondary component (associated with the back side). To make this robust, they use discminer-based model outputs as per-pixel initial guesses for peak intensity, line width, and centroid velocity, and they iterate: pixels where single-component fits are selected, or where fits fail, or where fitted widths are implausibly narrow relative to the channel width, are re-fit using median parameter values from a local neighborhood (an 11×11 grid) of successful fits. They report that the number of flagged pixels is a small fraction (less than 10%) and stabilizes after 10 iterations.

The paper’s reported results are primarily best-fit geometric and dynamical parameters for the sample, plus methodological demonstrations of how the new extraction improves velocity precision. For example, the fitted Keplerian stellar masses from 12CO fiducial modeling range from 0.45 M⊙ (DM Tau) to 1.76 M⊙ (V4046 Sgr). Inclinations span from 19.4° (CQ Tau) up to 71.2° (DM Tau), with systemic velocities υLSRK ranging from about −2.33 km s−1 (HD 34282) to 7.72 km s−1 (HD 143006). The paper also provides emission-surface parameters for each tracer (z0, p, Rt, q) and specifies whether the front/back combination uses mask or sum for each tracer and disk. For instance, in HD 135344B the 12CO model uses a single-side approach (front/back not combined for that tracer in the table), while 13CO and CS are not modeled in the same way (the table indicates missing entries for some tracers), reflecting cases where the back side does not affect symmetry due to geometry or shallow vertical structure.

While the excerpt does not provide a single headline statistical test (e.g., a p-value for an improvement), the authors do provide quantitative diagnostics of fit quality in the velocity-map comparison: they discuss reduced χ2 values (with a reduced chi-squared definition) when comparing kernels and fitting strategies, and they show that single-component velocity maps (quadratic or Gaussian) can be contaminated by backside emission, especially on the near side, whereas the double-component moments are less affected and offer improved precision. They also highlight that the bell kernel with a line-slope parameter can reproduce Gaussian widths while matching the observed line-shape morphology; in their illustrative simulation, both profiles have a true amplitude of 40 K, and the bell kernel retrieves a width consistent with the Gaussian (bell width 0.41±0.01 km s−1) while slightly underestimating amplitude (38.4±0.9 K).

Limitations are acknowledged in several places. First, the discminer modeling assumes simplified parametric intensity and Keplerian dynamics and does not fully account for detailed physical structure or radiation transport; thus, derived parameters should be interpreted as effective quantities for fast exploration rather than fully physical reconstructions. Second, the noise model in the MCMC likelihood neglects spatial correlations, leading to underestimated uncertainties; the authors cite a factor of ~10 increase when correlations are included. Third, the two-surface approach for optically thin emission assumes emission is confined to a geometrically narrow region; if the emission slab is thick, layering effects can introduce additional non-thermal broadening and biases, though the authors argue CS is likely thin enough to mitigate this. Finally, the authors assume either fully optically thick or fully optically thin behavior across the disk for each tracer, rather than allowing a radial transition through marginal optical depth, which would require additional free parameters.

Practically, the implications are that exoALMA’s subsequent planet-hunting and disk-physics papers can rely on a more reliable baseline extraction of velocity maps and line-profile observables. This matters for anyone interpreting deviations from Keplerian rotation as planet-driven perturbations: the methodology reduces the risk that apparent “substructures” are artifacts of front/back overlap and fitting degeneracies. The results are most relevant to observational disk astronomers using ALMA line cubes, especially those analyzing inclined disks and optically thin tracers where backside contributions can strongly affect moment maps and derived kinematics. The pipeline also provides a standardized set of best-fit stellar masses, inclinations, position angles, systemic velocities, and emission-surface parameters that serve as inputs for the rest of the exoALMA series.

Overall, the paper’s core contribution is a robust, model-informed extraction framework that explicitly treats front/back overlap in inclined disks and uses tracer-dependent optical-depth assumptions to improve the fidelity of velocity and intensity measurements from molecular line data.