Applying a Particle-only Model to the HL Tau Disk

TL;DR

This study demonstrates that a simplified particle-only model can effectively approximate the structure of the HL Tau protoplanetary disk, aiding initial planetary parameter estimation before detailed hydrodynamic simulations.

Contribution

The paper introduces the application of a particle-only model, originally for debris disks, to a gas-rich protoplanetary disk, providing a computationally efficient method for initial disk and planet analysis.

Findings

Successfully matched HL Tau's radial profile with three embedded planets.

Derived planetary masses and orbital radii consistent with previous estimates.

Reproduced narrow gaps potentially caused by planet-disk interactions without requiring planets in those gaps.

Abstract

Observations have revealed rich structures in protoplanetary disks, offering clues about their embedded planets. Due to the complexities introduced by the abundance of gas in these disks, modeling their structure in detail is computationally intensive, requiring complex hydrodynamic codes and substantial computing power. It would be advantageous if computationally simpler models could provide some preliminary information on these disks. Here we apply a particle-only model (that we developed for gas-poor debris disks) to the gas-rich disk, HL Tauri, to address the question of whether such simple models can inform the study of these systems. Assuming three potentially embedded planets, we match HL Tau's radial profile fairly well and derive best-fit planetary masses and orbital radii (0.40, 0.02, 0.21 Jupiter masses for the planets orbiting a 0.55 solar-mass star at 11.22, 29.67, 64.23 AU). Our derived parameters are comparable to those estimated by others, except for the mass of the second planet. Our simulations also reproduce some narrower gaps seen in the ALMA image away from the orbits of the planets. The nature of these gaps is debated but, based on our simulations, we argue they could result from planet-disk interactions via mean-motion resonances, and need not contain planets. Our results suggest that a simple particle-only model can be used as a first step to understanding dynamical structures in gas disks, particularly those formed by planets, and determine some parameters of their hidden planets, serving as useful initial inputs to hydrodynamic models which are needed to investigate disk and planet properties more thoroughly.