effect

Jeans instability

Jeans instability is a gravitational instability in a gas cloud that leads to its collapse and the formation of stars or other structures.
13 related articles · 3 formulas · 1 who worked here

Description

In 1902, British physicist James Jeans examined the condition for gravitational collapse of a self-gravitating gas sphere. He realized that collapse begins when the free-fall time becomes shorter than the sound-crossing time. If a density perturbation cannot be smoothed out by sound, gravity locally amplifies it—an avalanche-like contraction ensues. From wave analysis in a homogeneous medium, a critical length λ_J ~ c_s / √(G ρ) is derived. Regions larger than λ_J are unstable. Thus nature automatically carves matter into stellar 'loaves'.

History

James Hopwood Jeans published his analysis of gravitational instability in 1902 within Newtonian gravity. He mathematically showed how small density perturbations in an infinite medium can grow if the wavelength exceeds a critical value. Later, the theory was generalized to account for the expansion of the Universe (E.M. Lifshitz in 1946) and relativistic effects. Modern observational data on star clusters and infrared images of star-forming regions brilliantly confirm the Jeans fragmentation scenario.

How it works

In astrophysics, Jeans instability is used to estimate collapse conditions for molecular clouds and the formation of planetary systems in protoplanetary disks. It is applicable to gas regions with weak magnetic fields and negligible rotation; under rapid rotation or strong magnetization, the critical mass increases. In cosmology, the Jeans length determines the scale at which primordial density perturbations begin to grow.

In practice

Jeans instability determines the threshold for interstellar cloud collapse into protostars and is used in numerical models of star formation.

Fun fact

The Sun itself once formed from a cloud fragment that lost Jeans stability about 4.6 billion years ago.

Concept graph →

Formulas

$$\Gamma_1 > \frac{4}{3} + k\frac{GM}{Rc^2}$$
Stellar stability requires adiabatic index above 4/3 plus GR correction.
What is in the formula
\Gamma_1variableFirst adiabatic index — adiabatic index
MvariableMass of the star — mass kilogram
RvariableRadius of the star — radius metre
cvariableSpeed of light — speed metre per second
GconstantNewtonian gravitational constant — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
kconstantNumerical constant of order unity depending on stellar structure — structure constant = 1
\gamma_{\rmcrit}\simeq\frac{4}{3}+c\frac{gm}{rc^2} · 2606.02539v1
$$k_J = \sqrt{\frac{4\pi G \rho}{c_s^2}}$$
Scale where thermal pressure supports against collapse.
What is in the formula
k_JvariableJeans wavenumber — wavenumber reciprocal metre
\rhovariableMass density — mass density kilogram per cubic metre
c_svariableSound speed — speed of sound metre per second
GconstantUniversal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared
k_j=\sqrt{\frac{8πgρ_0}{v_t^2}} · 2607.04893
$$M_J \propto \frac{T^{3/2}}{\rho^{1/2}}$$
Minimum mass for gravitational collapse overcoming thermal pressure.
What is in the formula
M_JvariableJeans mass, minimum mass for collapse — mass kilogram
TvariableTemperature of the gas — temperature kelvin
ρvariableMass density of the gas — mass density kilogram per cubic metre
m_j\propto\frac{t^{3/2}}{ρ^{1/2}} · 2607.04942v1

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