Physics Help Forum Collapse of the sun

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 Jul 12th 2008, 10:02 PM #1 Senior Member   Join Date: Apr 2008 Location: HK Posts: 886 Collapse of the sun If the sun collapses and changes to white dwarf, enormous amount of energy would be released as gravitational energy is converted to kinetic energy and heat. But I wounder why sun would collapse? What originally supporting the ground of sun has vanished? To what extent would the ground of sun fall towards the centre so that no more gravitational energy is lost?
Jul 13th 2008, 05:11 AM   #2

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 Originally Posted by werehk If the sun collapses and changes to white dwarf, enormous amount of energy would be released as gravitational energy is converted to kinetic energy and heat. But I wounder why sun would collapse? What originally supporting the ground of sun has vanished? To what extent would the ground of sun fall towards the centre so that no more gravitational energy is lost?
The Sun (or any star) has no surface in the traditinal sense. It is a fluctuating boundary set by the internal heat of the Sun and the gravitational force exerted at the surface boundary. Heat generated by the Sun was initially created by the gravitational collapse of a huge dust cloud, primarily composed of hydrogen. This heat eventually became large enough to set of fusion reactions on the hydrogen and the heat energy produced in that process has balanced the gravitational collapse since that point.

Eventually the Sun will begin to end its fusion process. There are actually several stages to this process, but basically what happens is that the Sun will get cooler and cooler and unable to support the gravitational forces causing its collapse. The Sun will collapse to the point where the repulsion of the electron clouds between the remaining atoms/molecules will couter-balance the gravitational collapse. The Sun will then become a white dwarf, fading to a brown dwarf as its temperature continues to fall.

The interesting thing is when the star has much more mass than the Sun. If the mass is large enough the gravitational force is too much for the electromagnetic repulsion of the electron clouds and the collapse continues. At some point the electrons are forced into the nucleus and the protons and electrons combine to form neutrons. At this point the neutrons, being fermions, repel each other via the exclusion principle: no two fermions may have the same quantum state. So the gravitational collapse is then halted, and the star becomes a neutron star.

The size of the force between the neutrons is also finite. So if the mass of the star is even larger than before it is possible that even this repulsion can be overcome. In this case our theories fail to predict what will happen, but it is clear that the gravitational collapse will continue even further. There is some speculation that the star could fall into a "quarkonium" state and become a theoretical object called a "quark star." No such star has yet been positively identified. The ultimate result is, of course, a black hole in which the gravitational collapse continues indefinitely. I should mention that black holes are impossible to observe at a distance and that the black holes that Astronomers have discovered are extremely massive objects that cannot be detected directly. These have similar properties in all ways to black holes, but we really don't know if they are or if they are something else.

-Dan
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 Jul 13th 2008, 08:56 PM #3 Senior Member   Join Date: Apr 2008 Location: HK Posts: 886 For a blackhole which is continuously collapsing, the radius of it is zero? But still blackhole is massive, is it only because of the extremely high mass? Does blackhole exists as a single point only?
Jul 14th 2008, 04:57 AM   #4

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 Originally Posted by werehk For a blackhole which is continuously collapsing, the radius of it is zero? But still blackhole is massive, is it only because of the extremely high mass? Does blackhole exists as a single point only?
You are now asking questions that are central to the heart of black hole research. Some say one thing, some say another.

According to Classical Physics deep inside the event horizon of a black hole lies an object called a "singularity." It is the end result of the collapse of an object into a black hole. It has infinite density and a zero radius.

Now, we get into some really strange effects when we factor in General Relativity. As the surface of the star collapses under gravity the acceleration of the surface increases until the surface reaches approximately the speed of light. (Which no object may travel faster than.) But any object traveling that close to the speed of light undergoes a time dilation and the time frame of this object "slows down" according to an outside observer. (A similar effect exists for an object moving in an extremely large gravitational field, so the falling surface gets a double whammy of time dilation.) Detailed calculations using the Schwartzchild solution to the General Relativity equations show that the suface of the star never quite reaches the event horizon: the surface takes an infinite amount of time to fall to the event horizon according to an observer outside of the forming black hole. So the Universe has never had enough time to form the singularity. (The really cool thing is that if you are an observer dropping along with the surface of the star then you will pass through the event horizon. As you look back up at the rest of the Universe their time frame has "sped up" and you can see how the Universe will end.)

This is not to say that no black holes have formed: for all intents and purposes any object that has collapsed under the effect of gravity like that has the same properties as a "traditional" black hole would. So we are effectively arguing about the number of angels that fit on the head of a pin.

But the lack of the physical singularity is, to my mind, critical. Not only does a state of infinite mass density and zero radius not make any logical sense, the equations of Physics really really really really have problems with it. (And please note that all fundamental subatomic particles have these same features according to the Standard Model: they are what we call "point particles" and this fact has remained a thorn in the side of Physicists since the early 1900s. Hence the interest in String Theory (which has no experimental basis) which predicts a non-zero size for these particles. So the problem of the singularity is not a feature of Astronomy alone.)

To answer your second question, if we had the right equipment, we could collapse a marble to a black hole. Any object denser than (about) the density of neutronium (the material inside a neutron star) will collapse under its own gravitational influence. In fact, the Standard model suggests that mini-black holes may have formed early on in the Big Bang. Such black holes are predicted to have the mass of, say, a mountain. So black holes do not need to have ridiculously large masses.

By the way, to clear up a common misconception about black holes: they have no more gravitational influence as any other object with the same mass. For example, if the Sun were to collapse to a black hole (and didn't lose any mass in the process as it would if the Sun went supernova) the planets of the Solar System would quite happily remain in their orbits: they would not be sucked into the black hole. The thing about the black hole is that you can get much much closer to the center of mass than you can with the Sun, so the gravitational acclerations you will feel from the black hole can be much much larger.

-Dan
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