Using Structure Functions to Characterize Protoplanetary Disk Velocity Residuals
Abstract
Protoplanetary disks, the birthplace of planetary systems, are highly dynamic environments. High angular and spectral resolution observations have revealed non-Keplerian motions in nearly every source studied, indicative of (magneto-)hydrodynamical instabilities or planet-disk interactions. However, these velocity perturbations rarely exhibit ordered structure, limiting our ability to attribute them to a specific mechanism. We propose the second-order structure function as a tool for recovering structural properties of velocity perturbations in the presence of significant noise. Using morphological models, we demonstrate how easy-to-calculate heuristics and parametric model fits together identify structure in noisy data and recover its properties, including correlation lengths, their radial scaling where genuinely present, and the anisotropy. We further outline a workflow to de-noise the data and to build a matched null model against which inferences are compared. Applying the framework to one numerical simulation each of the gravitational, magneto-rotational and vertical-shear instabilities, we recover their structure at high significance and the structural heuristics separate all three pairs, with the gravitational and vertical-shear instability simulations remaining the hardest to distinguish once observationally degraded. As a demonstration on real data, 12CO observations of TW Hya reveal azimuthally elongated velocity structure that persists once the large-scale m=1 component is removed. We also delineate where a Gaussian description breaks down for coherent features such as spiral arms, and how inclination affects the recovered heuristics. The methodology is implemented in the eddy package and provides a foundation for statistically characterizing turbulent velocity structure in high-resolution disk observations.
Related
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- Radiation Hydrodynamics of Self-gravitating Protoplanetary Disks II. Accretion, Migration, Spin, and Internal Structure of GI Fragments
BibTeX
@misc{teague2026using,
title = {{Using Structure Functions to Characterize Protoplanetary Disk Velocity Residuals}},
author = {Richard Teague and Sean M. Andrews and Jaehan Bae and Marcelo Barraza-Alfaro and Abigail Bodner and Jonathan D. Henshaw and Giovanni Rosotti},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07305},
eprint = {2611.07305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Using Structure Functions to Characterize Protoplanetary Disk Velocity Residuals
AU - Richard Teague
AU - Sean M. Andrews
AU - Jaehan Bae
AU - Marcelo Barraza-Alfaro
AU - Abigail Bodner
AU - Jonathan D. Henshaw
AU - Giovanni Rosotti
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07305
UR - https://arxiv.org/abs/2611.07305
AB - Protoplanetary disks, the birthplace of planetary systems, are highly dynamic environments. High angular and spectral resolution observations have revealed non-Keplerian motions in nearly every source studied, indicative of (magneto-)hydrodynamical instabilities or planet-disk interactions. However, these velocity perturbations rarely exhibit ordered structure, limiting our ability to attribute them to a specific mechanism. We propose the second-order structure function as a tool for recovering structural properties of velocity perturbations in the presence of significant noise. Using morphological models, we demonstrate how easy-to-calculate heuristics and parametric model fits together identify structure in noisy data and recover its properties, including correlation lengths, their radial scaling where genuinely present, and the anisotropy. We further outline a workflow to de-noise the data and to build a matched null model against which inferences are compared. Applying the framework to one numerical simulation each of the gravitational, magneto-rotational and vertical-shear instabilities, we recover their structure at high significance and the structural heuristics separate all three pairs, with the gravitational and vertical-shear instability simulations remaining the hardest to distinguish once observationally degraded. As a demonstration on real data, 12CO observations of TW Hya reveal azimuthally elongated velocity structure that persists once the large-scale m=1 component is removed. We also delineate where a Gaussian description breaks down for coherent features such as spiral arms, and how inclination affects the recovered heuristics. The methodology is implemented in the eddy package and provides a foundation for statistically characterizing turbulent velocity structure in high-resolution disk observations.
ER -