Are All Stars the Same Size Due to Nuclear Fusion?

[TonyTT]

Why are all stars not the same size? Given that the nuclear fusion within a star begins when the pressure/temperature in the core of a collapsing cloud reaches certain parameters, why are all stars not the same size?

 

[Vanadium 50]

Why would collapsing clouds be the same size?

 

[Naty1]

A basic answer to your question is that the universe of NOT perfectly homogeneous and never has been. But initially it was a lot more so than now...

So conditions change from place to place, and not every planet, nor asteroid, nor star is identical to every one of its counterparts. So even tiny initial differences which we believe are basic in our universe can add up to huge variations later on.

Check here for a vivid photo of such clouds leading to star formation:
http://en.wikipedia.org/wiki/Formation_of_stars#Stellar_nurseriesJeans instability is one factor in star formation:

http://en.wikipedia.org/wiki/Jeans_mass

This tells us variations pressure and density affect star formation. Sounds a little like a black hole formation...but
just a little.

 

[mrspeedybob]

I think the OP raises a good question. It seems like once a star reached critical mass and fusion ignited the resulting solar wind would push the remaining gas away. If more fusionable material fell into the star the increased rate of reaction would result in more solar wind which would further limit what fell in. This should result in the vast majority of stars being near the smallest possible size.

I think the answer lies in the fact that gravity also increases with mass. This would have 3 effects.

First it is a stronger counter force to the repulsive effect of the solar wind.

Second, the solar wind itself looses more momentum as it climbs out of the gravity well, and thus looses repulsive force.

Third, as the stars gravity increases time dilation results in less solar wind being produced then would be without time dilation. If doubling a stars mass increases its energy output per unit time by 12 fold, then it's energy output per unit time as observed from a distance would increase by less then 12 fold because more time elapses at a distance form the star. The same energy output is spread over more time.

Disclaimer: I not an astrophysicist. The above is slightly educated speculation.

 

[Ken G]

It sounds to me like there are really two separate questions here, and it's not obvious which one is being asked. The first question is, why don't all stars have the same mass, if they all "turn on" when the core reaches similar temperatures? The answer to that is, the mass that a star will end up having gets determined long before the core reaches fusion temperature, so there is no direct connection between the conditions when fusion starts, and the mass of the star.

The second question is, given that stars can have different masses, should we still expect them to be the same size (i.e., same radius) if the temperature of the core is similar? The answer to that is, no-- the mass of the star should directly affect its size, even if the core temperatures are similar. That's because gravity heats the star as it contracts, but a higher mass star has a stronger gravity when it has the same size as a lower mass star, so it also heats more (when it's at the same size), so it reaches fusion temperatures when it is still much larger. Lower mass stars must gravitationally contract much more to reach fusion temperatures, and that is why they are smaller. (Ironically, by the time they contract enough to fuse, their densities and gravities end up larger than the high-mass stars. When people forget that, they end up saying all kinds of crazy things like high-mass stars are more luminous because their cores are denser or have stronger gravity or pressure, all of which is not true about the cores of high-mass stars.)

 

[SpiffyKavu]

Speedy: time dilation in any of these systems is negligible. The core would have to approach the size of a black hole for the given mass for time dilation to have any affect, and thermal pressure will prevent that long before contraction can reach that stage.

The the question of how do stars of different masses form is still partially unanswered. Stars around 1 solar mass is easy for the models to form. We have recently been able to form lower mass stars in these models by including smaller-scale physics such as interactions with magnetic fields and turbulence and things. High mass stars are still problematic in the models.

 

[Chronos]

Large gas clouds tend to fragment when they collapse due to Jeans instability, hence extremely massive stars are rare and multiple star systems are very common. It is believed the mass of a star ceases to increase once fusion initiates.