The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) III: The vertical structure of debris disks

TL;DR

ARKS presents high-resolution ALMA Band 7 observations of 24 debris disks, focusing on the most highly inclined targets to recover their vertical dust distributions. By applying both parametric and nonparametric modeling (including frank and rave) and rigorous model selection via AIC/BIC, the study finds a broad range of vertical structures, with h_HWHM spanning ~0.003 to ~0.19 and a common preference for thick-tailed vertical profiles, such as Lorentzian or multi-component distributions. The results imply diverse dynamical states, with several disks containing masses comparable to or less than Neptune and many consistent with self-stirring or planetary perturbations as stirring mechanisms, and they reveal potential two-population dynamical structures in multiple systems. Comparisons with scattered-light measurements and theoretical considerations suggest that non-Gaussian vertical distributions may be common, possibly reflecting Neptune-like migration histories or long-term planet-disk interactions, and motivate higher-resolution, multiwavelength follow-up to refine constraints on disk masses, stirring, and planet presence.

Abstract

Debris disks -- collisionally sustained belts of dust and sometimes gas around main sequence stars -- are remnants of planet formation processes and are found in systems ${\gtrsim}10$ Myr old. Millimeter-wavelength observations are particularly important, as the grains probed by these observations are not strongly affected by radiation pressure and stellar winds, allowing them to probe the dynamics of large bodies producing dust. The ALMA survey to Resolve exoKuiper belt Substructures (ARKS) is analyzing high-resolution observations of 24 debris disks to enable the characterization of debris disk substructures across a large sample for the first time. For the most highly inclined disks, it is possible to recover the vertical structure of the disk. We aim to model and analyze the most highly inclined systems in the ARKS sample in order to uniformly extract the vertical dust distributions for a sample of well-resolved debris disks. We employed both parametric and nonparametric methods to constrain the vertical dust distributions for the most highly inclined ARKS targets. We find a broad range of aspect ratios, revealing a wide diversity in vertical structure, with a range of best-fit parametric values of $0.0026 \leq h_{\rm HWHM} \leq 0.193$ and a median best-fit value of $h_{\rm HWHM}=0.021$. The results obtained by nonparametric modeling are generally consistent with the parametric modeling results. We find that five of the 13 disks are consistent with having total disk masses less than that of Neptune (17 $M_{\oplus}$), assuming stirring by internal processes (self-stirring and collisional and frictional damping). Furthermore, most systems show a significant preference for a Lorentzian vertical profile rather than a Gaussian.

Figures (12)

• Figure 1: Gallery of the data (left), models (center), and residuals (right, with model contours overplotted for reference) for the fiducial parametric vertical structure models for each source (models shown in Table \ref{['tab:formsshort']}). The effective beam is denoted by the shaded ellipse in the bottom-left corner of each panel, and the scale bars in the bottom right of each panel are 50 au in length. In the data and model panels, contours show three, five, seven, and nine times the rms (positive in light gray, negative in dark gray). In the residual panels, the purple and orange contours show $+3$ and $-3$ times the rms, respectively, though none of the sources show significant structure in the residuals. For each source, the data and model images are plotted on the same color scale, which spans the full dynamic range of each data image.
• Figure 2: Comparison of the fiducial vertical profiles for each disk at the reference radius $R_{\rm{ref}}$, defined as the location of peak intensity in the fiducial model (Table \ref{['tab:masses']}). Sources are ordered by $H_{\rm HWHM}(R_{\rm{ref}})$ and divided into two panels for visual clarity, with disks with $H_{\rm HWHM}(R_{\rm{ref}})<15$ au in the top panel and disks with $H_{\rm HWHM}(R_{\rm{ref}})>15$ au in the bottom panel. We denote extended or multi-component vertical profiles with asterisks (one asterisk for a Lorentzian profile, and two asterisks for a double Gaussian vertical profile). The remaining sources have Gaussian vertical profiles. Colored lines and the shaded regions denote the median profile $\pm 1 \sigma$, while the dashed black lines show the best-fit model. The thick horizontal black bars show the nominal resolution of the interferometer, $\lambda_{\rm obs}/b_{\rm max}$, where $\lambda_{\rm obs}$ is the observing wavelength and $b_{\rm max}$ is the longest baseline in the array. The thin horizontal black bars show the width of one beam along the vertical axis of the disk using the images shown in Figure \ref{['fig:dmr_gallery']}.
• Figure 3: Posterior distributions of the vertical aspect ratios for the fiducial parametric models. The histograms and KDEs are shown in light and dark purple, respectively. The median $h_{\rm HWHM}$ is shown by the vertical black line. The dark blue dashed line shows the 16th and 84th percentiles (equivalent to $1 \sigma$ for Gaussian distributions), while the light blue dotted line shows the 0.15th and 99.85th percentiles (equivalent to $3 \sigma$ for Gaussian distributions). Since the fiducial model for HD 10647 has two distinct vertical components, we show the posterior distributions for both $h_{\rm HWHM1}$ (top center panel) and $h_{\rm HWHM1}$ (top right panel).
• Figure 4: Top: Arbitrary Gaussian, Lorentzian, and double Gaussian profiles that demonstrate how a Lorentzian can mimic a double Gaussian without the extra model parameters. The Gaussian (blue line) and Lorentzian (black line) profiles have a FWHM of 2 au, while the double Gaussian (orange dotted line) is composed of one Gaussian with a FWHM of 1.7 au and another with a FWHM of 6 au. Bottom: Various exponential forms with different $\zeta$ (colored lines, $\zeta$ values annotated on the panel). The wings of the Lorentzian (black line) are closely matched with an exponential with $\zeta=1$. All profiles are normalized to the same maximum value.
• Figure 5: Stirring disk masses obtained from the Pan_2012 stirring model with the fiducial $h_{\rm HWHM}$ measurements for both the gas-bearing (square) and gas-poor (circles) debris disks. The color bar corresponds to the parametrically derived fractional widths ($\Delta R/R$) presented in Han_2026. We took the average $\Delta R/R$ for disks with multiple reported rings (HD 15115 and HD 197481). The upper panel shows a histogram of disk masses in our sample overlaid with a KDE (purple line).