Forming Stars: 2 Conditions and Criteria Explained

[thegirl]

2 conditions to form a star
- all atoms in the gas cloud must be gravitationally bound to each other (so the virial theorem applies)
- the cloud must permanently lose overall energy

E=-GMm/2R therefore R=-GMm/2E, so for R to become smaller and the energy to also become smaller the energy needs to be negative. Besides this reason, why would the energy be increasingly negative? Is the energy of the cloud negative to begin with?

Also, Unstable gas clouds do not become star as they cannot continually lose energy, does anyone know why this is? Why can't unstable gas clouds continually lose energy what makes them different to stable gas clouds?

Cooling time determines wether a cloud goes into free fall without pressure support or if it will heat the nebula adiabatically (which is where no heat enters or leaves the system). Does anyone know the criteria which distinguishes the two? Wether it'll be one or the other?

Sorry for all the questions. Thanks in advance.

 

[marcus]

I'd say the ability to radiate away heat would be one thing that makes a cloud stable. I'm no expert in star formation, and I expect someone with expert knowledge will see your question and give a neat concise answer. But I think it is an interesting question, so I'll tell you what occurs to me.

Contracting means the potential energy (which is negative) gets more negative. By the virial theorem that means the cloud has to blow off kinetic energy.

The way that would typically happen is you have inelastic collisions between the molecules that causes them to shake, rattle, and roll. This causes the molecules to radiate in the EM spectrum, infrared, microwave, whatever.

Molecules are better at doing this than individual, say Helium, atoms. Molecules have more parts to start banging and jiggling when they collide so they are better at inelastic collisions and radiating heat.
I think. As I say I'm not an expert.

 

[marcus]

Another thing that occurs to me. Suppose the cloud is so big that THE HEAT HAS TROUBLE GETTING OUT
because the outer layers are effectively opaque to whatever radiation is being generated deeper in.

You asked what makes a cloud stable (able to contract to form a star) versus one that is unstable (has serious trouble contracting).
I'm trying to think what would make it easy, and what would make it hard.

BTW are you interested in the "dark matter" component? Do you want that to enter the picture? Or do you want to keep it simple and just have the cloud be ordinary matter?

Are you interested in clouds that jettison excess energy by flinging parts of themselves off into space? That would seem like a kind of "unstable" behavior, for a cloud. But there must be clouds of this or that stuff which actually do that: Parts get ejected with very high KE so that the KE of the remainder can decline and permit continued collapse.

 

[thegirl]

omg! thank you so much, you just cleared up a world of misunderstanding with the whole negative energy becoming more negative. I'd just like to keep things as simple as possible at the moment, and yes I didn't really consider the cloud being so big.

one last question? Would you say that negative work has been done by gravity in bringing the material together and if so why?

Thank you again!

 

[Ken G]

Would you say that negative work has been done by gravity in bringing the material together and if so why?

The sign of the work done by gravity would generally not be regarded as negative. Perhaps marcus has not gotten around to this question, so I will jump in. Energy is conserved, so work never makes any energy increase or decrease, all it does is convert from one form to another. What is going on here is called the "work/energy theorem", which says that work is the way to get other forms of energy to be converted into kinetic energy, or vice versa. The sign convention is that positive work is "done by" a system if it loses kinetic energy, and work is done "on" the system if the system gains kinetic energy (this is the reason we define the concept of kinetic energy in the first place, it is often easy to keep track of work done by a force field). The work/energy theorem says that the way to change the kinetic energy is by applying a force over a displacement (which is like a distance), and if a force is applied in the direction of the displacement, that is called positive work "done on" the system, and will increase the system kinetic energy. So when a system contracts, positive work is being done "on" the system "by" gravity, and the kinetic energy of the system is increasing. The total energy of the system is decreasing though, because that also includes the negative potential energy, and the light being radiated away requires that the total energy of the system must drop, because energy is conserved when all forms are included. So we can say that positive work is being done by gravity, but only half that work is staying in the kinetic energy of the system, the other half is being radiated away-- and that latter half is the reason the work is being done by gravity in the first place, ironically.

 

[thegirl]

You explained it so well! Thank you so much!