The vertical structure of debris discs and the role of disc gravity: A primer using a simplified model

Antranik A. Sefilian; Kaitlin M. Kratter; Mark C. Wyatt; Cristobal Petrovich; Philippe Thébault; Renu Malhotra; Virginie Faramaz-Gorka

doi:10.1093/mnras/staf1555

paper

The vertical structure of debris discs and the role of disc gravity: A primer using a simplified model

arXiv:2505.09578 · doi:10.1093/mnras/staf1555

Abstract

Debris discs provide valuable insights into the formation and evolution of exoplanetary systems. Their structures are commonly attributed to planetary perturbations, serving as probes of as-yet-undetected planets. However, most studies of planet-debris disc interactions ignore the disc's gravity, treating it as a collection of massless planetesimals. Here, using an analytical model, we investigate how the vertical structure of a back-reacting debris disc responds to secular perturbations from an inner, inclined planet. Considering the disc's axisymmetric potential, we identify two dynamical regimes: planet-dominated and disc-dominated, which may coexist, separated by a secular-inclination resonance. In the planet-dominated regime ( $M_{d} / m_{p} ≪ 1$ ), we recover the classical result: a transient warp propagates outward until the disc settles into a box-like structure centered around the planetary orbit's initial inclination $I_{p} (0)$ , with a distance-independent aspect ratio $H (R) \approx I_{p} (0)$ . In contrast, in the disc-dominated regime ( $M_{d} / m_{p} ≳ 1$ ), the disc exhibits dynamical rigidity, remaining thin and misaligned, with significantly suppressed inclinations and a sharply declining aspect ratio, $H (R) \propto I_{p} (0) R^{- 7/2}$ . In the intermediate regime ( $M_{d} / m_{p} ≲ 1$ ), the system exhibits a secular-inclination resonance, leading to long-lived, warp-like structures and a bimodal inclination distribution, containing both dynamically hot and cold populations. We provide analytic formulae describing these effects as a function of system parameters. We also find that the vertical density profile is intrinsically non-Gaussian and recommend fitting observations with non-zero slopes of $H (R)$ . Our results may be used to infer planetary parameters and debris disc masses based on observed warps and scale heights, as demonstrated for HD 110058 and $β$ Pic.

Accepted for publication in MNRAS; 29 Pages, 13 Figures, 1 Table

The vertical structure of debris discs and the role of disc gravity: A primer using a simplified model

Abstract

References in corpus (45)

Cited by in corpus (6)