Jeans instability

The Jeans instability is a concept in astrophysics that describes an instability that leads to the gravitational collapse of a cloud of gas or dust. It causes the collapse of interstellar gas clouds and subsequent star formation. It occurs when the internal gas pressure is not strong enough to prevent the gravitational collapse of a region filled with matter. It is named after James Jeans.

For stability, the cloud must be in hydrostatic equilibrium, which in case of a spherical cloud translates to

d

p

d

r

=

−

G

ρ

(

r

)

M

enc

(

r

)

r

2

,

{\displaystyle {\frac {dp}{dr}}=-{\frac {G\rho (r)M_{\text{enc}}(r)}{r^{2}}},}

where

M

enc

(

r

)

{\textstyle M_{\text{enc}}(r)}

is the enclosed mass, p is the pressure,

ρ

(

r

)

{\textstyle \rho (r)}

is the density of the gas (at radius r), G is the gravitational constant, and r is the radius. The equilibrium is stable if small perturbations are damped and unstable if they are amplified. In general, the cloud is unstable if it is either very massive at a given temperature or very cool at a given mass; under these circumstances, the gas pressure gradient cannot overcome gravitational force, and the cloud will collapse. This is called the "Jeans collapse criterion".

The Jeans instability likely determines when star formation occurs in molecular clouds.

History

In 1720, Edmund Halley considered a universe without edges and pondered what would happen if the "system of the world", which exists within the universe, were finite or infinite.