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I have been trying to find an answer to this question for some time. Just when I think I may have a definitive answer, something happens to change it. Is there a physical limit, in solar masses, to the size of a star?
Since the discovery of the Pistol Star in the Quintuplet Cluster near the galactic center in the early 1990s, it was thought that 150 solar masses was the upper limit. With the study of the Arches Cluster by astronomer Donald Figer, at the Rochester Institute of Technology in 2007, he suggests that 150 solar masses is the upper limit of stars in the current era of the universe.
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Figer used Hubble's Near Infrared Camera and Multi-Object Spectrometer to study hundreds of stars ranging from six to 130 solar masses. Although Figer did not find any stars larger than 130 solar masses, he conservatively set the upper limit at 150 solar masses. The Arches cluster is a youngster about 2 to 2.5 million years old. It resides 25,000 light-years away from Earth in our galaxy's hub, a hotbed of massive star formation. In this region huge clouds of gas collide to form behemoth stars.
...
Figer estimated the stars' masses by measuring the ages of the cluster and the brightness of the individual stars. He also collaborated with Francisco Najarro of the Instituto de Estructura de la Materia in Madrid, Spain. Najarro produced detailed models to confirm the masses, chemical abundances and ages of the Arches cluster stars. "Standard theories predict 20 to 30 stars with masses between 130 and 1,000 solar masses," Figer explained. "But we found none. If they had formed, we would have seen them," he added.
Figer cautions the upper limit does not rule out the existence of stars larger than 150 solar masses. His next step is to pinpoint more clusters to test his weight limit.
That seemed to be a definitive answer to my question. Then I stumbled upon this 2010 study of R136a1 in the open cluster NGC 3603, in the Carina spiral arm of the Milky Way, some 20,000 light-years away from the Solar System. R136a1 is estimated to currently be 265 solar masses, and was originally 320 solar masses, but has slowly shed around 55 solar masses over time. The paper suggest that stars up to 500 solar masses are possible.
The really interesting thing about these hyper-giants is the way they die. Unlike super-giants that go out in Type II Supernova and leave behind black holes, these monsters (above 130 solar masses) creates a "pair instability supernova" and leaves nothing behind.
This would also suggest that stellar black holes are only formed by stars in the 10 to 130 solar mass range.
The above study also suggests that hyper-giants, such as R136a1, have a life-span of less than 1.5 million years.
In the early universe, some 30 million years after the Big Bang, the first Population III stars formed, and were as big as 1,000 solar masses (in theory), or even bigger. However, their life-span would have been less than a million years, and none now exist. At a certain point, when the gas cloud finally compresses enough to start nuclear fusion, the solar winds would clear out any remaining gas in its immediate neighborhood, thereby being self-limiting in size. The question is, what is that limit?
It's hard to say. Part of the problem is that we've by no means observed all the stars in the universe. There are too many. Another problem is that we can't see beyond the particle horizon (the limit of the observable universe). The actual universe is thought to extend much farther out with objects that have long crossed the horizon which will never be seen as the space of the universe continues to expand.
It's hard to say. Part of the problem is that we've by no means observed all the stars in the universe. There are too many. Another problem is that we can't see beyond the particle horizon (the limit of the observable universe). The actual universe is thought to extend much farther out with objects that have long crossed the horizon which will never be seen as the space of the universe continues to expand.
I was hoping there was some sort of limit, like the Chandrasekhar limit which undergoes a gravitational collapse when a white dwarf reaches 1.44 solar masses. The metallicity of the gas cloud that forms the star must have some sort of limiting effect on mass of the star before it reaches nuclear fusion.
It might be a resolution problem where they are actually seeing a binary star close together. Dunno really.
They're calculating the mass from a theoretical model so perhaps some caution might be required using the model on unusual cases.
That is a very good point. I went back to the paper I posted in the OP and found this in the abstract:
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We consider the predicted X-ray luminosity of the R136 stars if they were close, colliding wind binaries. R136c is consistent with a colliding wind binary system. However, short period, colliding wind systems are excluded for R136a WN stars if mass ratios are of order unity.
I know there are a lot of super-massive binary pairs in the Quintuplet Cluster, but the biggest star in that cluster is between 80 and 150 solar masses.
I was hoping there was some sort of limit, like the Chandrasekhar limit which undergoes a gravitational collapse when a white dwarf reaches 1.44 solar masses. The metallicity of the gas cloud that forms the star must have some sort of limiting effect on mass of the star before it reaches nuclear fusion.
Is there a limit to the mass of a main-sequence star? I would argue there has to be some limit, but I don't think it's an important limit. Unlike white dwarfs, stars balance thermal pressure against gravity. On the main sequence above about 20 solar masses, the mass-luminosity relationship is roughly linear (as it is radiation pressure that is keeping them from gravitational collapsing). The luminosity-temperature relationship is L ~ T^4, so we can approximate the mass-temperature relationship for big stars as T~M^1/4. The exact power and constants aren't too important, only that they're power-law and not logarithmic relationships. As mass increases arbitrarily, the temperature necessary to support the star increases arbitrarily. As there are definite temperature limits for the stability of matter, there must be some theoretical limit to the mass of a star.
I'm not knowledgeable enough of astronomy nor smart enough to derive for myself what that limit is (quark-gluon plasma temperature? planck temperature? something lower in temperature) but I know there must be some limit. Unlike the Chandrasekhar and Tolman-Oppenheimer-Volkoff limits, however, whatever it is probably isn't that useful, because it will be crazy big. I think a more practical limit is how much mass can ever get close compacted in a small enough area to form something that could be called a star. I think that's the limit that really sets the largest stars out there; this is backed-up by the small numbers of really massive stars. It's likely any theoretical limit will have to be derived and not observed.
It might be a resolution problem where they are actually seeing a binary star close together. Dunno really.
They're calculating the mass from a theoretical model so perhaps some caution might be required using the model on unusual cases.
There are stars that look like a single star, but have turned out to be binary stars. Alpha Centauri looks like a single star to the naked eye, but it's a binary system (Alpha Centauri A and Alpha Centauri B). Adding to the fray is a third star called Proxima Centauri, which is thought to be gravitationally associated with the other two, and would make it a triple star system.
You raise a good point though. With more distant galaxies, it's harder to make out individual stars except for the brightest. Resolution and magnification are limiting, but those seem to be gradually improving with more powerful equipment and better techniques. There are some truly gigantic monsters out there.
I was hoping there was some sort of limit, like the Chandrasekhar limit which undergoes a gravitational collapse when a white dwarf reaches 1.44 solar masses. The metallicity of the gas cloud that forms the star must have some sort of limiting effect on mass of the star before it reaches nuclear fusion.
If there is a limit, I'm not familiar with what it is. Like you said in the OP, just when you think you've got a definitive answer, something comes along to change it.
It would seem like there would have to be some kind of limit. But it also seems to me that the upper limits are based on the largest known at the time. You may have already seen this article about the subject featuring R136a1 as the most extreme. The article states, "Our new finding supports the previous view that there is also an upper limit to how big stars can get, although it raises the limit by a factor of two, to about 300 solar masses." That should hold the record unless something more massive is discovered to raise the bar.
I'm sure you're right that the nebula is a contributing factor in terms of what's available before a star reaches nuclear fusion. The question is how much of a limiting factor is it? The article indicates 300 solar masses.
Is there a limit to the mass of a main-sequence star? I would argue there has to be some limit, but I don't think it's an important limit. Unlike white dwarfs, stars balance thermal pressure against gravity. On the main sequence above about 20 solar masses, the mass-luminosity relationship is roughly linear (as it is radiation pressure that is keeping them from gravitational collapsing). The luminosity-temperature relationship is L ~ T^4, so we can approximate the mass-temperature relationship for big stars as T~M^1/4. The exact power and constants aren't too important, only that they're power-law and not logarithmic relationships. As mass increases arbitrarily, the temperature necessary to support the star increases arbitrarily. As there are definite temperature limits for the stability of matter, there must be some theoretical limit to the mass of a star.
I agree that it is not logarithmic, and while it may seem arbitrary I believe it has more to do with the composition of the star. All the very young super-giant stars have low metallicity, as a percentage of their mass, similar to the very old Population II stars. Stars that are fusing hydrogen into helium do not have to burn as hot as stars fusing helium into carbon and oxygen. Also, the mass of a star determines how it will eventually die.
Under 3 solar masses and the star eventually becomes a white dwarf;
Between 3 and 10 solar masses and the star eventually becomes a neutron star;
Between 10 and 130 solar masses and the star eventually becomes a black hole;
Above 130 solar masses and the star eventually goes through a pair instability supernova and leaves nothing behind.
So how would a star with 500 solar masses die? Would it be any different than a star with more than 130 solar masses? If Population III stars could reach 1,000 solar masses or more in the early universe, would we be able to see the remnants of their deaths? How would they die?
I really do not expect answers to my questions ... yet.
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Originally Posted by jayrandom
I'm not knowledgeable enough of astronomy nor smart enough to derive for myself what that limit is (quark-gluon plasma temperature? planck temperature? something lower in temperature) but I know there must be some limit. Unlike the Chandrasekhar and Tolman-Oppenheimer-Volkoff limits, however, whatever it is probably isn't that useful, because it will be crazy big. I think a more practical limit is how much mass can ever get close compacted in a small enough area to form something that could be called a star. I think that's the limit that really sets the largest stars out there; this is backed-up by the small numbers of really massive stars. It's likely any theoretical limit will have to be derived and not observed.
That is exactly what I would like to know. Once gravity condenses the gases enough so that nuclear fusion begins, at that point the "star," or proto-star, is not going to grow appreciably. Its own solar winds will push away the remaining gases. A few more objects will undoubtedly plunge into the star, but not enough to increase its mass by much. Unless, it is another star.
In some of the other very old globular clusters, they are finding very young stellar giants. They surmised, none have been observed, that these "very young" giants are the result of two very old stars colliding and combining their mass.
If two super-giants, in excess of 150 solar masses, were to collide ... never-mind. I will not go there.
200 Solar Masses for a stable star......is the absolute maximum I'm aware of.....(anything much heavier....about 250 Solar Masses quickly collapses into a Black Hole)
Last edited by PITTSTON2SARASOTA; 06-18-2012 at 08:43 PM..
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