What is the significance of the Jeans length in cloud collapse?

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SUMMARY

The significance of Jeans length in cloud collapse is defined by the formula λj = √(15kBT / (4πGμP)), where μ represents the average mass per particle in the gas cloud. This average is typically calculated based on the composition of the gas, which is approximately 75% hydrogen and 25% helium. Understanding this concept is crucial for astrophysicists studying the stability and collapse of interstellar clouds, as it provides a quantitative measure for gravitational instability.

PREREQUISITES
  • Understanding of astrophysical concepts such as gravitational collapse
  • Familiarity with thermodynamics, specifically the Boltzmann constant (kB)
  • Knowledge of basic fluid dynamics and pressure (P) in astrophysical contexts
  • Grasp of the concept of average mass per particle (μ) in a gas mixture
NEXT STEPS
  • Research the implications of Jeans length on star formation processes
  • Study the role of temperature (T) in gravitational stability
  • Explore the effects of varying gas compositions on Jeans length calculations
  • Learn about numerical methods for solving n-body problems in astrophysics
USEFUL FOR

Astrophysicists, cosmologists, and students studying gravitational dynamics and star formation in interstellar clouds will benefit from this discussion.

AbsoluteZer0
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Hello,

As I understand, the following formula describes the Jeans length.

\lambda_j = \sqrt\frac{15k_BT}{4\pi G \mu P}

Where \mu is the mass per particle.

Forgive me if this question may come across as relatively stupid, I imagine that each of the particles within the cloud should have different masses. Is \mu an average of the masses?
 
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Yeah it is, but since most gas is generally ~75% H and ~25% He or something close to that, it's easy to figure out the average mass per particle.
 
It's one of those n-body things where you must approximate to get a numerical solution.
 

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