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 \leavevmode \nobreak M _ { \odot } 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 .