English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Several mechanisms have been identified that create dense particle clumps inthe solar nebula. The present work is concerned with the gravitational collapseof such clumps, idealized as being spherically symmetric. Calculations usingthe two-fluid model are performed (almost) up to the time when a centraldensity singularity forms. The end result of the study is a parametrization forthis time, in order that it may be compared with timescales for variousdisruptive effects to which clumps may be subject. An important effect is thatas the clump compresses, it also compresses the gas due to drag. This increasesgas pressure which retards particle collapse and leads to oscillation in thesize and density of the clump. The ratio of gravitational force to gas pressuregives a two-phase Jeans parameter, $J_t$, which is the classical Jeansparameter with the sound speed replaced by an the wave speed in a coupledtwo-fluid medium. Its use makes the results insensitive to the initial densityratio of particles to gas as a separate parameter. An ordinary differentialequation model is developed which takes the form of two coupled non-linearoscillators and reproduces key features of the simulations. Finally, aparametric study of the time to collapse is performed and a formula (fit to thesimulations) is developed. In the incompressible limit $J_t \to 0$, collapsetime equals sedimentation time. As $J_t$ increases, the collapse time decreasesroughly linearly with $J_t$ until $J_t \gtrsim 0.4$ when it becomesapproximately equal to the dynamical time.

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