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

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In summary, the formula for the Jeans length is described as \lambda_j = \sqrt\frac{15k_BT}{4\pi G \mu P}, where \mu represents the average mass per particle. This is an approximation used in solving for the numerical solution in n-body problems, where gas is typically composed of ~75% H and ~25% He.
  • #1
AbsoluteZer0
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Hello,

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

[itex] \lambda_j = \sqrt\frac{15k_BT}{4\pi G \mu P} [/itex]

Where [itex] \mu [/itex] 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 [itex] \mu [/itex] an average of the masses?
 
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  • #2
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.
 
  • #3
It's one of those n-body things where you must approximate to get a numerical solution.
 

1. What is the "Jeans length" in astrophysics?

The Jeans length is a characteristic length scale in astrophysics that describes the minimum size at which a cloud of gas can collapse under its own gravitational force. It is named after British physicist James Jeans, who first proposed this concept in 1902.

2. How is the Jeans length calculated?

The Jeans length is calculated using the Jeans mass, which takes into account the density, temperature, and pressure of the gas cloud. It can be expressed as λJ = √(πcs^2/Gρ), where cs is the sound speed, G is the gravitational constant, and ρ is the gas density.

3. What is "cloud collapse" in astronomy?

Cloud collapse is the process by which a large, diffuse cloud of gas and dust in space collapses under its own gravity, forming denser regions and eventually leading to the formation of stars and planets. This process is crucial in the formation and evolution of galaxies.

4. What factors affect the Jeans length and cloud collapse?

The main factors that affect the Jeans length and cloud collapse are the temperature, density, and pressure of the gas cloud, as well as the presence of any external forces such as magnetic fields or turbulence. These factors can determine whether the cloud will collapse or disperse.

5. What are the implications of understanding Jeans length and cloud collapse?

Understanding the Jeans length and cloud collapse is important for studying the formation of stars and galaxies, as well as the evolution of the universe. It can also help us predict the locations and characteristics of newly forming stars and planets. Additionally, this knowledge can aid in our understanding of the physical processes that govern the behavior of matter in space.

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