The Spherically Symmetric Gravitational Collapse of a Clump of Solids in a Gas

Abstract

Several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Calculations using the two-fluid model are performed (almost) up to the time when a central density singularity forms. The end result of the study is a parametrization for this time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject. An important effect is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure which retards particle collapse and leads to oscillation in the size and density of the clump. The ratio of gravitational force to gas pressure gives a two-phase Jeans parameter, $J_t$, which is the classical Jeans parameter with the sound speed replaced by an the wave speed in a coupled two-fluid medium. Its use makes the results insensitive to the initial density ratio of particles to gas as a separate parameter. An ordinary differential equation model is developed which takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit $J_t\to 0$, collapse time equals sedimentation time. As $J_t$ increases, the collapse time decreases roughly linearly with $J_t$ until $J_t\gtrsim 0.4$ when it becomes approximately equal to the dynamical time.

References in corpus (20)

• Rapid planetesimal formation in turbulent circumstellar discs
• Streaming Instabilities in Protoplanetary Disks
• Coagulation, fragmentation and radial motion of solid particles in protoplanetary disks
• The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? II. Introducing the bouncing barrier
• Protoplanetary Disk Turbulence Driven by the Streaming Instability: Non-Linear Saturation and Particle Concentration
• Particle Clumping and Planetesimal Formation Depend Strongly on Metallicity
• Towards planetesimals: dense chondrule clumps in the protoplanetary nebula
• Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation
• Size-selective concentration of chondrules and other small particles in protoplanetary nebula turbulence
• Heavy particle concentration in turbulence at dissipative and inertial scales
• Final Stages of Planet Formation
• Towards Initial Mass Functions for Asteroids and Kuiper Belt Objects
• Dust sedimentation and self-sustained Kelvin-Helmholtz turbulence in protoplanetary disk mid-planes. I. Radially symmetric simulations
• Turbulent pair dispersion of inertial particles
• On Gas-Drag Induced Rapid Migration of Solids in a Non-Uniform Solar Nebula
• On linear dust-gas streaming instabilities in protoplanetary discs
• DID PLANET FORMATION BEGIN INSIDE PERSISTENT GASEOUS VORTICES?
• Three-Dimensional Simulations of Kelvin-Helmholtz Instability in Settled Dust Layers in Protoplanetary Disks
• Jumping the Gap: The Formation Conditions and Mass Function of Pebble-Pile Planetesimals
• Constraining Galactic Magnetic Field Models with Starlight Polarimetry

Cited by in corpus (9)

• Dust evolution in protoplanetary discs and the formation of planetesimals. What have we learned from laboratory experiments?
• Turbulence sets the length scale for planetesimal formation: Local 2D simulations of streaming instability and planetesimal formation
• Efficient planet formation by pebble accretion in ALMA rings
• Cascade Model for Planetesimal Formation by Turbulent Clustering
• Jumping the Gap: The Formation Conditions and Mass Function of Pebble-Pile Planetesimals
• Survival of ALMA Rings in the Absence of Pressure Maxima
• Linking planetesimal and dust content in protoplanetary disks via a local toy model
• Aggregate Growth and Internal structures of Chondrite Parent Bodies Forming from Dense Clumps
• Planetesimal gravitational collapse in a gaseous environment: Thermal and dynamic evolution