Jeans instability

Cmertin

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?

Yuu Suzumi

Dear Cmertin,

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

All the best,
Yuu