Understanding Jeans Instability & Masses

In summary, the Jeans instability is a phenomenon in astrophysics that describes the collapse of a gas cloud due to gravitational forces. The Jeans mass and length are important parameters in this process and are calculated using the average molecular mass, temperature, and density of the gas cloud. The formula for the Jeans mass is [itex]M_{J}=(\frac{5×k_{B}×T}{G×μ×m_{H}})^{1.5}×(\frac{3}{4×\Pi×\rho_{0}})^{.5}[\itex]. It is important to note that this formula may not work for very large objects in space and may require additional adjustments.
  • #1
Cmertin
58
0
I'm trying to understand all the properties of the Jeans instability, the Jeans mass and the Jeans length. I understand the mathematics behind it, though not all the variables. There is a [itex]m_{H}[\itex] or I've also seen it as [itex]m_{p}[\itex] in the Jeans length and Jeans mass. The formula is as follows:

[itex]M_{J}=(\frac{5×k_{B}×T}{G×μ×m_{H}})^{1.5}×(\frac{3}{4×\Pi×\rho_{0}})^{.5}[\itex], I know that μ is the average molecular mass.

Can someone help me understand this please? I'm a bit confused. I tried looking at the units, though couldn't figure it out.

Also, another question about it: Does it work for all masses of ISM? From what I picked up in class, most things don't work for very large objects in astro, and they need more "fudge factors" to work. Is that the same for the Jeans instabilities?
 
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  • #2
Dear Cmertin,

H stands for hydrogene, p for proton. The nass measured in that unit is [itex]\mu[/itex]!

All the best,
Yuu
 

1. What is Jeans Instability?

Jeans Instability is a physical phenomenon in which a system of particles, such as gas or dust, becomes unstable and collapses under its own gravitational force.

2. How does Jeans Instability contribute to the formation of stars and galaxies?

Jeans Instability is one of the key processes in the formation of stars and galaxies. It allows for the collapse of gas clouds and the formation of dense cores, which eventually become stars. On a larger scale, Jeans Instability is also responsible for the collapse of gas and dust clouds into galaxies.

3. What factors affect the critical mass for Jeans Instability?

The critical mass for Jeans Instability is affected by several factors, including the temperature and density of the gas or dust, the speed of sound in the medium, and the size of the system. Higher temperatures and densities, as well as smaller systems, will result in a lower critical mass for instability.

4. How is the critical mass for Jeans Instability related to the mass of a star or galaxy?

The critical mass for Jeans Instability is directly related to the mass of a star or galaxy. The collapse of a gas cloud due to Jeans Instability will result in the formation of a star with a mass equal to or slightly larger than the critical mass. Similarly, the collapse of a larger gas cloud will result in the formation of a galaxy.

5. Can Jeans Instability occur in other systems besides gas and dust clouds?

Yes, Jeans Instability can occur in other systems besides gas and dust clouds. It can also occur in systems of particles such as stars, planets, or even on a molecular level. Any system with a significant amount of mass and self-gravitational force can experience Jeans Instability.

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