Gravito-turbulent bi-fluid protoplanetary discs: 1. An analytical perspective to stratification
arXiv:2503.13136 · doi:10.1051/0004-6361/202453434
Abstract
Context. In Class 0/I and the outskirts of Class II circumstellar discs, the self-gravity of gas significantly affects the disc's vertical hydrostatic equilibrium. The contribution of dust, whose measured mass is still uncertain, could influence this equilibrium. Aims. We aim to formulate and solve approximately the equations governing the hydrostatic equilibrium of a self-gravitating disc composed of gas and dust. Particularly, we aim to provide a fully consistent treatment of turbulence and gravity, affecting almost symmetrically gas and dust. Observationally, we study the possibility of indirectly measuring disc masses through gas layering and dust settling measurements. Methods. We used analytical methods to approximate the solution of the 1D Liouville equation with additional non-linearities governing the stratification of a self-gravitating protoplanetary disc. The findings were verified numerically and validated through physical interpretation. Results. For a constant vertical stopping time profile, we discovered a nearly exact layering solution valid across all self-gravity regimes for gas and dust. From first principles, we defined the Toomre parameter of a bi-fluid system as the harmonic average of its constituents' Toomre parameters. Based on these findings, we propose a method to estimate disc mass through gas or dust settling observations. We introduce a generic definition of the dust-to-gas scale height, applicable to complex profiles. We also identified new exact solutions for benchmarking self-gravity solvers in numerical codes. Conclusions. The hydrostatic equilibrium of a gas/dust mixture is governed by their Toomre parameters and effective relative temperature. This equilibrium could be used for measuring disc masses, improving our understanding of disc settling and gravitational collapse, and enhancing the computation of self-gravity in thin disc simulations.
References in corpus (53)
- Streaming Instabilities in Protoplanetary Disks
- Nonlinear Outcome of Gravitational Instability in Cooling, Gaseous Disks
- ALMA Survey of Lupus Protoplanetary Disks I: Dust and Gas Masses
- Gravitational Instabilities in Circumstellar Disks
- Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration
- Radial Flow of Dust Particles in Accretion Disks
- Linear and nonlinear evolution of the vertical shear instability in accretion discs
- Dust and Gas in the disc of HL Tauri: Surface density, dust settling, and dust-to-gas ratio
- Disks ARound TTauri Stars with Sphere (DARTTS-S) I: Sphere / IRDIS Polarimetric Imaging of 8 prominent TTauri Disks
- Spiral Density Waves in a Young Protoplanetary Disk
- Why do protoplanetary disks appear not massive enough to form the known exoplanet population?
- Direct mapping of the temperature and velocity gradients in discs. Imaging the vertical CO snow line around IM Lupi
- Evidence for a correlation between mass accretion rates onto young stars and the mass of their protoplanetary disks
- Global Models for the Evolution of Embedded, Accreting Protostellar Disks
- Observations of edge-on protoplanetary disks with ALMA I. Results from continuum data
- Measuring turbulent motion in planet-forming disks with ALMA: A detection around DM Tau and non-detections around MWC 480 and V4046 Sgr
- The Radial Distribution of Dust Particles in the HL Tau Disk from ALMA and VLA Observations
- Convective Overstability in radially stratified accretion disks under thermal relaxation
- Mapping accretion and its variability in the young open cluster NGC 2264: a study based on u-band photometry
- Three-Dimensional Vortices in Stratified Protoplanetary Disks
- Hot H2O Emission and Evidence for Turbulence in the Disk of a Young Star
- Molecules with ALMA at Planet-forming Scales (MAPS) IV: Emission Surfaces and Vertical Distribution of Molecules
- Treating gravity in thin disk simulations
- A highly settled disk around Oph 163131
- Global MHD simulations of stratified and turbulent protoplanetary discs. II. Dust settling
- Turbulence sets the length scale for planetesimal formation: Local 2D simulations of streaming instability and planetesimal formation
- Gas and dust dynamics in starlight-heated protoplanetary disks
- Estimate on dust scale height from ALMA dust continuum image of the HD 163296 protoplanetary disk
- Self-Replicating Three-Dimensional Vortices in Neutrally-Stable Stratified Rotating Shear Flows
- Resonant drag instability of grains streaming in fluids
- Distribution of solids in the rings of the HD 163296 disk: a multiwavelength study
- The Flying Saucer: Tomography of the thermal and density gas structure of an edge-on protoplanetary disk
- Modeling protoplanetary disk SEDs with artificial neural networks: Revisiting the viscous disk model and updated disk masses
- A dynamical measurement of the disk mass in Elias 2-27
- Protoplanetary Disk Masses from Radiative Transfer Modeling: A Case Study in Taurus
- Directly tracing the vertical stratification of molecules in protoplanetary disks
- Testing the Jeans, Toomre and Bonnor-Ebert concepts for planetesimal formation: 3D streaming instability simulations of diffusion regulated formation of planetesimals
- Dynamical mass measurements of two protoplanetary discs
- Gravitational instability in a planet-forming disk
- A novel way of measuring the gas disk mass of protoplanetary disks using N2H+ and C18O
- Gas temperature structure across transition disk cavities
- Large-scale CO spiral arms and complex kinematics associated with the T Tauri star RU Lup
- Rotation curves in protoplanetary disks with thermal stratification
- Mapping Protoplanetary Disk Vertical Structure with CO Isotopologue Line Emission
- The Anatomy of an Unusual Edge-on Protoplanetary Disk. II. Gas temperature and a warm outer region
- The Anatomy of an Unusual Edge-on Protoplanetary Disk I. Dust Settling in a Cold Disk
- Constraining turbulence in protoplanetary discs using the gap contrast: an application to the DSHARP sample
- Particle Dynamics in 3D Self-gravitating Disks II: Strong Gas Accretion and Thin Dust Disks
- Weighing protoplanetary discs with kinematics: physical model, method and benchmark
- Primordial dust rings, hidden dust mass, and the first generation of planetesimals in gravitationally unstable protoplanetary disks
- Self-gravity in thin discs and edge effects: an extension of Paczynski's approximation
- Self-gravity in thin-disc simulations of protoplanetary discs: smoothing length rectified and generalised to bi-fluids
- Traveling wave solutions for wave equations with two exponential nonlinearities