Formation of Stars: Questions on Range & Equilibrium

[Brunolem33]

Recently watching a documentary about stars (how the universe works), I was wondering about two things.

The first one is: how is it possible to have stars with such a wide range of sizes?

As far as I understand, stars are created in swirling gas clouds, nebulae.
When the accumulation of gas reaches a certain density and heat, with the help of gravity, a star is "ignited".
Yet, why do some "gas clouds" ignite as soon as they reach, say, the size of the sun, while others need to be ten or a hundred time bigger?

Why isn't there some kind of tipping point at which ignition should automatically occur, making all stars pretty much similar in size? is this related to the composition of the gas cloud, or something else?

The second question is: how is it possible that, despite vast differences regarding gravity and fusion conditions inside small and big stars, they all manage to maintain equilibrium between attraction and repulsion forces?

It looks like the increase of the gravitational force, from a small to a big star, is compensated by a "fine tuning" of the fusion process, so that the repulsion force is increased just enough, so that equilibrium is always preserved, no matter the size of the star.

How likely is that?

 

[stoomart]

I watch this show too and I think it often gets too speculative, like you can tell they are dragging the physicists into discussing remote "possibilities".

Why isn't there some kind of tipping point at which ignition should automatically occur, making all stars pretty much similar in size? is this related to the composition of the gas cloud, or something else?

My understanding is the "ignition" requires several conditions, which are discussed here in Wikipedia's Star formation article. As for how big they get, it just depends on how much matter they have available to consume.
I don't understand your second question, but I can say that the star remains stable as long as it has enough fuel to drive fusion, or until it produces iron and kills itself.

 

[Drakkith]

The first one is: how is it possible to have stars with such a wide range of sizes?

Unfortunately that's hard to answer in a short post. At least for me. But I can try to answer some of your specific questions.

As far as I understand, stars are created in swirling gas clouds, nebulae.
When the accumulation of gas reaches a certain density and heat, with the help of gravity, a star is "ignited".
Yet, why do some "gas clouds" ignite as soon as they reach, say, the size of the sun, while others need to be ten or a hundred time bigger?

Well, the simple explanation is that larger protostars have more matter than smaller protostars. This matter takes up room and the forming protostar can't collapse into as small of a volume as a smaller, less massive protostar. It's not that large protostars need to be bigger to reach the temperature required to fuse hydrogen, it's that they simply have more matter and are thus larger in size when they finally reach those temperatures.

The second question is: how is it possible that, despite vast differences regarding gravity and fusion conditions inside small and big stars, they all manage to maintain equilibrium between attraction and repulsion forces?

The equilibrium situation is a self-correcting process. If you could magically exert a compressive force over the entire surface of the star, the star would collapse very slightly, the temperature would increase, and this increase in temperature would exert an outward force that would resist your compressive force. The fusion rate would increase as well thanks to the increase in temperature.

It looks like the increase of the gravitational force, from a small to a big star, is compensated by a "fine tuning" of the fusion process, so that the repulsion force is increased just enough, so that equilibrium is always preserved, no matter the size of the star.

How likely is that?

It's a simple consequence of the fact that a hot gas exerts pressure on itself and any container it may be in (which is why you shouldn't leave containers of compressed air or other gases out in the Sun). For a star this manifests as a force which opposes gravity and holds the star up against collapse.

 

[rootone]

All stars are the result of large clouds of interstellar gas and dust, mostly Hydrogen, collapsing under gravity.
At some stage Hydrogen fusion will occur tending to arrest the collapse, but if the collapsing cloud is sufficient massive it can still add further material to the new star.

 

[Brunolem33]

Thanks, Drakkith I think you answer my questions...

 

[Ken G]

There is still a part of the question which has not been answered, because there isn't yet an answer. If you throw a cookie at the floor, it will splinter into lots of crumbs of various sizes. It is perhaps not so surprising that there would be a distribution there, given the complexity of the cookie-crumbling process. Similarly, it is perhaps not surprising that there should be a wide variety of stellar masses. Remember that the mass is determined long before there is any trace of nuclear ignition.

But if one wants to understand the distribution in masses that you do see, that's a whole different matter, and is probably as complicated as the crumbling of a cookie. I'm not aware of any theory that explains either one, but one can hope that there is some kind of principle at play that transcends all the complex details.

 

[stoomart]

Remember that the mass is determined long before there is any trace of nuclear ignition.

Can you expound on this a bit further? Is it the same as Drakkith's second paragraph above?

 

[Drakkith]

Can you expound on this a bit further? Is it the same as Drakkith's second paragraph above?

I think Ken means that the mass of the forming protostar is determined by the complex dynamics of the collapsing gas and dust cloud (aka a molecular cloud). Well before fusion begins the cloud has already collapsed and formed dozens to thousands of dense regions, each of which will end up as a star. To quote wikipedia: https://en.wikipedia.org/wiki/Star_formation#Cloud_collapse

As it collapses, a molecular cloud breaks into smaller and smaller pieces in a hierarchical manner, until the fragments reach stellar mass. In each of these fragments, the collapsing gas radiates away the energy gained by the release of gravitational potential energy. As the density increases, the fragments become opaque and are thus less efficient at radiating away their energy. This raises the temperature of the cloud and inhibits further fragmentation. The fragments now condense into rotating spheres of gas that serve as stellar embryos.

 

[Chronos]

Large, collapsing gas clouds tend to fragment into smaller clumps. The size of these clumps is determined by a complex process that depends on composition, environment and undoubtedly a host of other factors not entirely yet understood. Collectively, these factors form what is commonly referred to as the stellar initial mass function [IMF]. For a review of this interesting subject see; https://arxiv.org/abs/1001.2965, A Universal Stellar Initial Mass Function? A Critical Look at Variations.