Gravitational collapse of a turbulent vortex with application to star formation

Details Gravitational collapse of a turbulent vortex with application to star formation Gravitational collapse of a turbulent vortex with application to star formation

Oct 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976apj...209..190d&link_type=abstract

Astrophysical Journal, vol. 209, Oct. 1, 1976, pt. 1, p. 190-204.

Astronomy and Astrophysics

Astrophysics

7

Axial Flow, Gravitational Collapse, Pressure Effects, Protostars, Star Formation, Turbulent Flow, Density Distribution, Equations Of Motion, Gravitational Fields, Partial Differential Equations, Poisson Equation, Similarity Theorem, Spatial Distribution, Taylor Series, Velocity Distribution, Vorticity

Scientific paper

The gravitational collapse of a rotating cloud or vortex is analyzed by expanding the dependent variables in the equations of motion in two-dimensional Taylor series in the space variables. It is shown that the gravitational and rotational terms in the equations are of first order in the space variables, the pressure-gradient terms are of second order, and the turbulent-viscosity term is of third order. The presence of turbulent viscosity ensures that the initial rotation is solid-body-like near the origin. The effect of pressure on the collapse process is found to depend on the shape of the initial density disturbance at the origin. Dimensionless collapse times, as well as the evolution of density and velocity, are calculated by solving numerically the system of nonlinear ordinary differential equations resulting from the series expansions. The axial flow is always inward and allows collapse to occur (axially) even when the rotation is large. An approximate solution of the governing partial differential equations is also given in order to study the spatial distributions of the density and velocity.

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