Molecular cloud-Jeans law-Bonnar-Ebert model

[phigla]

Good morning,

I'm trying to understand the collapse and fragmentation of a molecular cloud leading to a proto=star.
I read about the Jeans law .and now about the Bonnar Ebert model.
As an example I took a molecular cloud of 10^4 solar mass, a temperature of 10K, 1000 particles by cm^3 (taking a mu of 2.33 the density become 3.9 10^17 kg/m^3
Using the Jeans law It leads me nowhere
If I use the Bonnar-Ebert model can it show me something ?
What is the difference between this two method ?
I will be happy if a member is patient enough to explain to me
Thanks in advance and best regards

Philippe

 

[Helio]

I know too little to be of any technical help. But that rarely stops me from trying.

The Jeans Instability simply gives the tipping point, when equilibrium is lost. Equilibrium is when the gas pressure equates to the gravitational attraction. You can Google for that somewhat simple equation.

You can chose your own radius outward from whatever you wish to make the densest region(s). If the gravitational side of the equation becomes stronger than the pressure side, collapse begins for that region.

It takes, however, something to trigger the cloud into suddenly finding itself, after millions or billions of years, to be unstable. Supernovae certainly are powerful triggers, but supersonic flows within gas clouds are well known and can lead to instability.

 

[phigla]

Thanks Helio,
I'm not a specialist, reason I'm on this forum...to try to understand
With the example I tell in my question, the molecular cloud collapse. If it collapse the number of particles remaining the same, as the radius will decrease therefore the volume as well giving that the density of the collapsed cloud will increase.
It will remain isotherm so the collapse will continue but till when ?
When the fragmentation will start ?
Maybe I'm wrong in my logic
Reason why i need some help
Regards

 

[Helio]

With the example I tell in my question, the molecular cloud collapse. If it collapse the number of particles remaining the same, as the radius will decrease therefore the volume as well giving that the density of the collapsed cloud will increase.

Yes.

It will remain isotherm so the collapse will continue but till when ?

In general, as it collapses it will begin to compress and become warmer.

When the fragmentation will start ?

Something has to trigger it. Some sort of regional compression from the shockwave of a SN or the shockwaves from its own supersonic internal flows.