How do we get stars so much more massive than the Sun?

[zuz]

When a cloud of gas reaches a critical density, thermonuclear reaction occurs and a star is born. all other gas is blown away by the staller wind. So how do we get stars so much more massive then the sun?

 

[Simon Bridge]

The question contains it's own answer: when a cloud of gas reaches critical density, thermonuclear reaction occurs and a star is born.
Stars more massive than the sun happen when a very massive gas cloud reaches critical density.

The trick here is the definition of "excess".
I am guessing you have assumed that "excess" means all that part of the cloud that is not at critical density ... but this cannot be correct, since there would be no planets in that scenario. It follows that there is a mistaken assumption in the question.

Some of the cloud gets blown away by the ignition reaction ... but not all of it does.
What determines how much of the gas gets blown away?

Hint: escape velocity.

 

[sophiecentaur]

I have read that the angular momentum of the original nebula is relevant. The proportion of the nebula that ends up as part of the star will depend on the rotation rate (slower would produce bigger) whilst the rest of the material will end up as planets, to account for the surplus angular momentum. I always wondered about this because, if it were true for established stars, there could be some very oblate stars about (only just hanging together), as far as I can see.
Perhaps this is nonsense? Someone on PF must know about this idea.

 

[anorlunda]

I have read that the angular momentum of the original nebula is relevant.

Yes Sophie, that's right. See the following paper. Shape is related to the ability to shed angular momentum.

The picture above is from a very entertaining paper, The Potato Radius: a Lower Minimum Size for Dwarf Planets

 

[sophiecentaur]

Yes Sophie, that's right. See the following paper. Shape is related to the ability to shed angular momentum.

Perhaps it would be hard to measure but it would be good to know if the distributions of rotation rate of stars actually correlates with their masses.
The situation for stars could be a bit different from that of objects without significant internal energy generation to 'pump them up.'

 

[Simon Bridge]

I was going to chime in that high oblateness stars exist... like http://www.eso.org/public/news/eso1147/
... very high rotation rates tend to be unstable, the angular momentum shedding thing. We do see super oblate objects out there though.

This is really at the fringe of my astrophysics.

Basically the simple model of star formation the op is exploring is incomplete. If that is zuz's point then zuz is correct.

 

[Chronos]

Unsurprisingly, the answer is complicated. The initial mass function [the technical term for the essential question] of stars is linked to metallicity and various other environmental factors in stellar birthing regions . The majority of stars tend to be small, like our sun. Red dwarfs [the lest massive class] are believed to comprise over 50% of all stars, whereas blue giants [the most massive of stars] are quite rare - on the order of 1 in a million. For further discussion see; https://arxiv.org/abs/astro-ph/0205466, The Stellar Initial Mass Function and Beyond

 

[sophiecentaur]

For further discussion see; https://arxiv.org/abs/astro-ph/0205466, The Stellar Initial Mass Function and Beyond

I could only read the abstract but does the paper deal with angular momentum? (It may be implied in some of it ). I guess it is not unreasonable to expect fewer really big ones. The main conclusion could be looked on as 'obvious' but then - nothing in cosmology is really obvious.

 

[stefan r]

I could only read the abstract...

Does this link work? It takes my computer/connection about 2 minute.

...does the paper deal with angular momentum? (It may be implied in some of it ). I guess it is not unreasonable to expect fewer really big ones...

My impression was that higher rotation rates increase the velocity of the stellar (main sequence) wind because of the magnetic field continues to accelerate particles. The stellar wind and interaction with interstellar gas carry angular momentum away from a star. Higher rotation main sequence stars are not ejecting that much more mass in the wind. With pre-main sequence stars something similar should happen. Herbig-haro objects are ejecting mass in a jet perpendicular to the spin axis. High rotation decreases pressure on the core which should decrease the nuclear reaction rate in the core. Also a flat object can radiate heat better than a spherical object.

I have read that the angular momentum of the original nebula is relevant. The proportion of the nebula that ends up as part of the star will depend on the rotation rate (slower would produce bigger) whilst the rest of the material will end up as planets, to account for the surplus angular momentum. I always wondered about this because, if it were true for established stars, there could be some very oblate stars about (only just hanging together), as far as I can see.
Perhaps this is nonsense? Someone on PF must know about this idea.

The pressure inside the nebula would be higher if the nebula is spinning slower. The R136 cluster has a mass of around 90,000 solar. The Tarantula Nebula was able to form the large stars in R136 because of compression. The Tarantula Nebula has around 450,000 solar mass. Most of the nebula will not end up as planets.

The rotation rate of stars formed in a nebula will be effected by the turbulence and the shape of the collapsed region. If a pair of stars that have low individual rotation rates merge the resulting star/object will have a high rotation rate. I believe an elongated fragment of a collapsing cloud will have more spin than a highly spherical

When a cloud of gas reaches a critical density, thermonuclear reaction occurs and a star is born. all other gas is blown away by the staller wind. So how do we get stars so much more massive then the sun?

The collapse occurs. The mass of the main sequence star is determined by the size of the cloud fragment. The cloud fragment's mass is much larger than the mass of the star it will become. All stars including brown dwarfs and type-Os will blow away a lot of gas as they collapse. Most of that blow out is finished when nuclear fusion. begins.
Protostar, still gathering mass
Pre-main sequence star, "has blown away surrounding material"
Stars larger than 8 solar mass can start fusion while they are still protostars but the energy is still lower than the energy of collapse.

 

[sophiecentaur]

Does this link work? It takes my computer/connection about 2 minute.

Yes, it works. Thanks. Plenty to get your teeth around in there!

 

[Ken G]

If you take a cookie and throw it on the ground, you get a range of sizes of crumbs. The details of exactly how you throw the cookie, or if you spin it, aren't terribly important-- there seems to be some kind of self-similar process that determines the distribution of sizes you get. Perhaps if you throw it harder, you may get smaller pieces on the whole, but you'll still get a range of relative sizes in which most pieces are smaller and few are larger, in relation to each other. Stars appear to be similar-- there is some complicated physics that determines the initial mass function, but the details don't seem to matter much because there is already so much going on that you get a kind of statistical outcome. No doubt angular momentum, initial magnetic fields, and metallicity can all be relevant factors, but they don't seem to matter that much unless they are very different from normal (such as the nearly zero metallicity of Big Bang gas, and so forth). What we are ultimately looking for is a kind of self-similar scaling law, not details in all the various different parameters. I don't believe an individual version of such a scaling law argument has been widely accepted, though various suggestions exist. But as with the cookie, you get lots of little pieces, and a few big ones, because there are simply more pathways that lead to small objects than to big ones. More ways to skin those cats, if you will.

Also, I believe the original question is motivated by a misconception about how star formation works. If you think all stars form inside-out, in the sense that they just build up larger and larger cores until the gravity is strong enough to release enough energy to start fusion, which then truncates the formation process and sets the mass of the star, then it is easy to imagine that all stars should have similar masses. But actually, the mass a star will have has normally been determined long before there is any fusion going on, and the mass that is blown away by a wind once fusion originates is not particularly important. Indeed, I'm not even sure where this idea originates that fusion onset begins a stellar wind, there just doesn't seem to be any credible reason why fusion in the center would have anything to do with wind from the surface. But even if that is true, and not simply an astrophysical urban legend (there are surprisingly many of those), the mass that can be driven in a wind is normally not important to the mass of a star (the current solar wind is particularly wimpy, but this is true for much stronger winds as well). It is better to think of the mass as being determined by a formation process that is unaware of the existence of fusion, but which ultimately tags what mass will end up in what star (like the crumbling cookie process does), in something more akin to an outside-in process in which information cascades down from large scales to smaller scales, rather than the other way around.

 

[Chronos]

I doubt that angular momentum plays any significant role on the stellar initial mass function. Were this not true it would be reasonable to expect a significant correlation between the velocity dispersion of maasive and low mass stars - especially in younger starburst regions of galaxies. No such disparity has been reported in the literature, as discussed here; https://arxiv.org/abs/1211.0543, Stellar mass versus velocity dispersion as tracer of the lensing signal around bulge-dominated galaxies . It is fairly well established that velocity dispersion is related to the momentum of the molecular gas clouds responsible for starburst activity and there is no apparent reason to suspect major angular momentum variance among otherwise similar gas clouds. The lack of any statistically significant difference in velocity dispersion between massive and low mass stars suggests it is of low relevance to the stellar initial mass function. It is also known that stars within the same cluster display little difference in their rotational velocity, as discussed here; https://arxiv.org/abs/astro- ph/0001065, The Angular Momentum Evolution of Very Low Mass Stars.

 

[JMz]

Perhaps it would be hard to measure but it would be good to know if the distributions of rotation rate of stars actually correlates with their masses.
The situation for stars could be a bit different from that of objects without significant internal energy generation to 'pump them up.'

Actually, it has been easy to measure stars' angular momentum for many decades: Even if you can't resolve the stellar disk, you can measure the width of spectral lines. Rapid rotation produces broad lines, just because the Doppler effect on one side of the disk will red-shift each line somewhat, and on the other side, blue-shift it. (Other effects can broaden them, too, but each effect produces a characteristic kind of broadening, so sufficiently precise measurements can distinguish the causes.)

Such high-rate stars are not rare. My recollection is that high-mass stars (before the red-giant stage) systematically have much more rapid rotation rates than the rest, though I have not followed that literature since pre-Hubble days. The speculation at that time was that lower-mass stars might, for whatever reason, systematically produce planets to a degree that high-mass ones did not; of course, with Kepler, we now have vastly better statistics on that.

 

[stefan r]

... My recollection is that high-mass stars (before the red-giant stage) systematically have much more rapid rotation rates than the rest, though I have not followed that literature since pre-Hubble days. The speculation at that time was that lower-mass stars might, for whatever reason, systematically produce planets to a degree that high-mass ones did not; of course, with Kepler, we now have vastly better statistics on that.

You recall correctly. High mass stars rotate faster. Old stars rotate slower and high mass stars do not become old. You can use a star's rotation rate to estimate the age.

Angular momentum is carried away by stellar winds. The magnetic field transfers momentum to particles.

 

[alantheastronomer]

High mass stars have shorter lifetimes because nuclear fusion in their cores proceeds at a faster rate, so even though they're more massive they last for a shorter time. Similarly, massive stars take a shorter time to form than low mass stars because their gravitational attraction is so much stronger. Stars of masses about 10 solar masses take about ten thousand years to reach their hydrogen burning phase on the main sequence, while low mass stars can take as long as a million years! Angular momentum is a significant part of this process. In fact, it throws a huge monkey wrench into the entire thing! When the protostellar cloud first forms from an initial density enhancement, it's hundreds of A.U.'s in size. As it contracts, angular momentum actually prevents the star from forming! What researchers think what happens next is that the magnetic field, formed by the protostar's ionized plasma's rotation, is "frozen" into the surrounding partially ionized protoplanetary disk, which is orbiting at a slower rate than the protostar's rotation, so that the effect is to increase the disk's rotation while slowing the star's in a process called "magnetic braking", allowing the star to finally form.

 

[Chronos]

This paper appears to put to rest any doubts about the role of angular momentum in the formation of massive stars; https://arxiv.org/abs/astro-ph/0604533, What Sets the Initial Rotation Rates of Massive Stars? Note in particular this assertion: "We find that the median of the quantity v_obs/v_c (observed rotational speed/equatorial breakup velocity) is typically about 0.15 and shows no evidence of a discontinuity over the full range of stellar masses...:"

 

[alantheastronomer]

This paper appears to put to rest any doubts about the role of angular momentum in the formation of massive stars; https://arxiv.org/abs/astro-ph/0604533, What Sets the Initial Rotation Rates of Massive Stars? Note in particular this assertion: "We find that the median of the quantity v_obs/v_c (observed rotational speed/equatorial breakup velocity) is typically about 0.15 and shows no evidence of a discontinuity over the full range of stellar masses...:"

You're misreading this article that you've posted - The value of 0.15 that you quote, is a RATIO, and the fact that it doesn't change from low mass to high mass stars just means that there's no different mechanism for forming low mass or high mass stars as explained in the article. Moreover, this ratio between "observed rotation rate" and "equatorial breakup velocity" being constant means that, since the "equatorial breakup velocity" increases with increasing mass,then the "observed rotation rate" also increases with increasing mass, which shows that there IS a correlation between angular momentum and stellar mass.