Vertical Structure of Protoplanetary Disks in Scattered Light: A large sample analysis

Abstract

High-resolution scattered-light imaging has revealed complex morphologies in protoplanetary and circumstellar disks. Measuring the vertical height of the scattering surface is key to understanding disk structure, evolution, and the properties of embedded dust. We develop a methodology for fitting elliptical shapes to scattered-light images of protoplanetary disks in order to extract vertical height profiles of the dust scattering surface across a large and morphologically diverse disk sample. The dataset consists of 92 near-infrared polarimetric images obtained with VLT/SPHERE. The aim is to identify trends in vertical structure across different disk morphologies and test for correlations with stellar mass, age, and disk dust mass, as well as to investigate the implications of the derived height profiles for the masses of potential embedded planets. We implement a structure extraction and ellipse fitting (SEEF) algorithm that uses edge detection and Gaussian fitting to locate disk structures. Ellipse fitting reveals spatial offsets between the ellipse centre and the stellar position, which are interpreted as vertical height assuming circular ring geometry. Disk inclination, position angle, and the aspect ratio h/r are also derived. The method yields vertical height measurements for 92 disks, showing profiles consistent with flared disk geometries. However, the full sample cannot be described by a single power-law relation. Subdivision by morphology shows no strong correlations for most disk classes, except for extended disks with outer radii larger than about 150 au, which exhibit a clear power-law flaring trend. The lack of strong correlations with other system properties suggests that either different morphologies exhibit distinct vertical structures or that additional physical factors influence disk flaring.

Figures (21)

• Figure 1: Gallery of representative disks from the sample, grouped by morphological geometry. Ellipse fits made in this study to the scattered-light disk structures are overplotted. The scale bar in each panel denotes 1 arcsecond.
• Figure 2: The distribution of year and filter within the initial dataset (totalling 294 images), showing a greater tendency towards H-band images.
• Figure 3: Left: An idealistic example of the edge detection method using a synthetic circumstellar disk with added Gaussian background noise. Radial cuts (dashed white lines) sample intensity profiles iteratively. Magenta dots mark detected disk edges where intensity first (measured inwards towards the star) exceeds a 5$\sigma$ noise primary threshold and passes the step function criteria. Edge labels are shown only on the right side of the disk (angles between 0$^\circ$ and 180$^\circ$ clockwise) for clarity. Background noise level ($\sigma$) and primary threshold (5$\sigma$) are annotated in the fig. Right: Radial intensity profile extracted at 180$^\circ$ from the centre of GM Aur in H-band, comparing the real high-S/N case (blue) and a synthetically degraded low-S/N case (orange). Horizontal dashed lines indicate the 5$\sigma$ and 3$\sigma$ primary thresholds used for edge detection. Step points used to confirm edge detection are marked with red crosses, and the final detected edge locations are indicated by vertical dashed-dotted lines and filled circles. The low-S/N profile shows degraded detection performance and premature truncation due to the outer edge being buried in noise.
• Figure 4: Aspect ratio ($h/r$) versus separation (r) for the structures within the 92 disks, with 133 measurements (rose). A power-law model of the form $h/r = A \left(\frac{r}{1\mathrm{au}}\right)^{\alpha - 1}$ was fit to the data using least squares (black). ($R^2$) is shown in the bottom-right corner. For comparison, power-law fits from Avenhaus2018 and Ginski_2016 are overlaid along with their corresponding data points in grey and light blue respectively.
• Figure 5: Two-panel visualisation of disk vertical height ($h$) and aspect ratio ($h/r$) as a function of separation ($r$) for the restricted dataset, with spiral and highly or lowly inclined disks excluded. Leaving extended, compact, and uniform disk types totalling 107 measurements. $R^2$ is shown in the bottom right of each plot. Top: Power-law fit to $h$ vs. $r$ shows an increasing vertical structure consistent with flaring. Bottom:$h/r$ vs. $r$ with power-law fits overlaid for this work (black), and comparison to Avenhaus2018 and Ginski_2016 in grey and light blue respectively.