exoALMA XX: Tomographic Detection of Embedded Planets in Protoplanetary Disks

Abstract

The exoALMA Large Program has revealed a wealth of substructures in the dust and molecular line emission of several protoplanetary discs, suggesting that planet formation may unfold within highly dynamic environments. Using synthetic observations of planet-disc interactions and disc instabilities, we demonstrate how the origin of these substructures can be investigated through a tomographic study of molecular lines, extending the scope of the analysis beyond line-centroid kinematics alone. Our results indicate that with only a few hours of ALMA integration at moderate angular resolution ($0.15''-0.30''$), it is possible to identify the key signatures driven by planets more massive than 0.1% of the stellar mass. These signatures manifest not only as deviations from Keplerian motion but also as localized line broadening, enabling accurate constraints on the orbital radius and azimuthal location of the planets. We further show that a diagnostic based on line skewness in spectrally resolved observations can help distinguish between planetary and instability-driven signatures, owing to the distinct degrees of velocity coherence associated with each mechanism. Finally, we apply this tomographic analysis to exoALMA CO line data for the discs of HD 135344B and MWC 758. In HD 135344B, we identify strongly localized velocity and line-width perturbations, suggesting the possibility of three massive planets embedded in the disc: one at $R=95$ au, exterior to the continuum substructures, and two within dust gaps at $R=41$ au and $R=73$ au. For MWC 758, the dominance of vertical-velocity spirals over localized signatures is consistent with predictions from models of moderate disc eccentricities or warps, potentially induced by a substellar companion in the inner regions of the system.

Figures (25)

• Figure 1: Velocity and line-width residuals derived from discminer models applied to synthetic observations of planet-disc interaction ($q=2\times10^{-3}$, $\phi_p=-45^\circ$) and disc instabilities. Details of the simulation setups are provided in Sect. \ref{['sec:planet_disc']}. All discs are inclined by $-30^\circ$, and the residuals from all mechanisms are shown on the same color scale indicated on the left. Semi red-blue circles in the bottom left corners of the top-row panels indicate the locations of the redshifted and blueshifted sides of the simulated disc, which are useful to understand the velocity structure of the non-Keplerian flows (see Fig. \ref{['fig:velocity_patterns']}).
• Figure 2: Illustrating axisymmetric velocity residuals for different combinations of velocity components, projected disc rotation, and the resulting folded maps obtained using either the additive or subtractive folding method. The first three columns show residuals for negative velocity flows after subtraction of a Keplerian model, while the following two focus on positive ones. In this context, positive denotes super-Keplerian motion for $v_\phi$, outward motion in cylindrical radius for $v_R$, and upward motion relative to the disc midplane for $v_z$. The rightmost column shows a scenario where the underlying disc emission surface includes a dip (30 au wide and 20 au deep) that is not considered by the subtracted model. This substructure introduces an anti-symmetric contribution to the residuals around the disc minor axis, which is consequently filtered out after additive folding.
• Figure 3: Illustration of the localized signatures identified in folded line-width and velocity residuals traced by $^{12}$CO emission from a planet-disc interaction simulation with a planet-to-star mass ratio of $q\!\sim\!2\times10^{-3}$, assuming a disc inclination of $i=-30^\circ$. Results are shown for two planet azimuths, $\phi_{p}=-45^\circ$ and $180^\circ$, and for two beam sizes, $0\hbox{$.\!\!^{\prime\prime}$}{3}$ and $0\hbox{$.\!\!^{\prime\prime}$}{15}$. Green circles and crosses mark the locations of peak and clustered residuals, while the unfilled circle denotes the true planet position. A signal is considered detected when its global peak exceeds a significance of 3$\sigma$, as indicated by the horizontal dotted and dashed lines, corresponding to thresholds defined using all peak residuals and the MAD estimator, respectively. Detections based on line widths have a higher success rate due to their stronger spatial localization (clustered residuals), compared to their velocity counterparts, which in this example remain undetected for the $\phi_p = -45^\circ$ planet and only marginally detected for $\phi_p = 180^\circ$. Since embedded planets are expected to produce localized line-width enhancements rather than reductions, the sign of the line-width signal also helps resolve the ambiguity between opposite sides of the disc introduced by the folding process.
• Figure 4: Detected amplitude of folded line-width perturbations as a function of the inferred planet azimuth in synthetic observations of the planet-disc interaction simulations introduced in Sect. \ref{['sec:planet_disc']}, for different planet masses and beam sizes, and a disc inclination of $i = -15^\circ$. Although increasing the beam size from $0\hbox{$.\!\!^{\prime\prime}$}{15}$ to $0\hbox{$.\!\!^{\prime\prime}$}{3}$ weakens the observed signal around the planet, its detectability is not compromised, suggesting that relatively inexpensive ALMA observations are sufficient to robustly detect planets with 0.2% the mass of the star and marginally detect those with 0.1%. Line-width amplitudes shown as filled circles were measured using subtractive folding of the disc, whereas dotted circles, corresponding to planets located along the disc minor axis, were obtained using additive folding (followed by division by two) to avoid self-subtraction of the signal in the former method. Vertical lines indicate the true planet azimuths used in each of the eight simulation snapshots. Horizontal lines and shaded regions denote the median and standard deviation of the peak values, respectively, while hatched areas mark the median $3\sigma$ detection threshold for the low-mass planet simulations.
• Figure 5: Goodness of planet detections based on localized line widths across all disc inclinations, planet masses and azimuths, beam sizes, and signal-to-noise ratios (SNR) considered. Sub-squares represent the eight adopted planet azimuths (from $-135^\circ$ to $180^\circ$ in steps of $45^\circ$). A score of 1 corresponds to a planet detected at its true location with a significance of at least $3\sigma$. The score is defined as the product of three Gaussian functions evaluating the proximity of the detection in radial and azimuthal coordinates, as well as its significance. Planets with scores above 0.6 (blue sub-squares) are detected within their radial pressure bump and azimuthal sector, with a significance of at least $3\sigma$. Central sub-squares indicate the median score across all planet azimuths, with those exceeding 0.6 outlined in red to highlight the inclination-mass configurations where planet-driven line broadening is detectable for each adopted beam size and SNR.