Holding the Sun up
Published on Oct 7, 2006 at 7:57 pm.
16 Comments.
Filed under Sun.
The other day, someone asked me where the Sun’s energy comes from. Well, the simple answer is that it comes from nuclear fusion in its core. But, as with all things, real life is a bit more complicated. How does energy get into the Sun so that nuclear fusion can release it? Where did the hydrogen come from (a related question). How is it released? How does energy released in the core of the Sun make it out to the surface? Well, naturally, you can take a simple question and a simple answer and just confuse everyone to death. So, I got to thinking that perhaps I’d talk about some of the things going on near the middle of the Sun.
The Sun is a large ball of hydrogen and helium. Often I simplistically tell people that it is a big ball of gas, but the reality is that only the outermost parts of the Sun are a gas. Once you get deep enough into the Sun, though, the conditions are such that the hdrogen and helium are no longer a gas, but rather a plasma — a different state of matter. That actually turns out to be important to understanding how the Sun, or other stars, work.
All that hydrogen and helium has mass, so there is a huge gravitational attraction. The Sun has a mass of 1.99×1030 kg (nearly 333,000 times the mass of the Earth). This gravitational force compresses the elements making up the Sun. At first, they act like a gas and heat up. Heating it increases the pressure, which holds up the interior of the Sun under the enormous pressure of the vast amount of material over it. But, the heat generated by this compression eventually works its way out, and so the pressure drops, allowing gravity to compress the core of the Sun a bit more, heating it up some more until the pressure holds it up. This is called Kelvin-Helmholtz contraction, and this is what generates heat in protostars and brown dwarfs.
But, if a protostar has enough mass, then the hydrogen in its core gets compressed so close together with enough thermal energy that a nuclear reaction takes place. Through a process known as the proton-proton chain (the details of which I might put in another blog entry sometime), the hydrogen is converted into helium. In essense, four hydrogen nuclei fuse to form a helium nucleus. Now, you can see that some sort of reaction must be going on at the subatomic level because four protons become two protons and two neutrons (a helium nucleus). What happens is that two protons become two neutrons, two positrons, and two neutrinos. But, as I said, I can say more about this in a later entry. But, here’s an interesting point. Four hydrogen atoms have a total of 6.693×10-27 kg of mass, but one helium nucleus has only 6.645×10-27 kg of mass. This means that after the reaction, there is 0.048×10-27 kg missing after each reaction. This may be particularly surprising, since isolated neutrons actually have more mass than protons, so how can two protons and two neutrons weigh less that four protons???
Now, don’t try to answer this by saying that the neutrinos and positrons account for the missing mass, since neutrinos have so little mass that they don’t affect this, and the positrons are anti-electrons, and as soon as they hit an electron (almost immediately after they are given off), both they and the electrons annihilate each other and release pure energy. Ah, there lies part of the clue. 
This missing mass becomes energy. Albert Einstein showed us that energy and matter are equivalent through his famous equation E=mc2. Take the missing mass, multiply it by the speed of light squared, and you get the energy released in this reaction. So, each reaction releases a bit of energy. Enough reactions release enough energy to heat the interior of the Sun enough to hold it up against the weight of the material above. Every second about 600 million tons of hydrogen is converted into 596 million tons of helium. Four million tons per second become energy. This holds up the Sun. But, this energy doesn’t stay in the core of the Sun, it works its way out to the surface. The visible surface of the Sun is a temperatuer of about 5800 K, and at that temperature it is plenty hot enough to shine, radiating away this heat in the form of electromagnetic radiation: mostly visible, ultraviolet, and infrared light.
But, the energy doesn’t just work its way out, nor does it just heat the gasses near the center of the Sun. Remember, I said that it wasn’t really gas, anyway, it’s a plasma. What happens is that much of the energy is given off as gamma rays. Gamma rays and X-rays are very high energy electromagnetic waves. One can simplistically say that these high energy waves heat the interior of the Sun, but how do they do that? Well, they do that by a process known as Compton scattering, a process named after Arthur Compton. It turns out that at the microscopic level things act as both particles and waves. That is true of things that we normally think of as particles (electrons actually have a wavelength) and things that we think of as waves (particles of light, called photons, carry momentum and energy just like matter particles). Now, this really shouldn’t be a surprise if you think about it. Electromagnetic waves are energy, but we just said that energy and matter are equivalent. Is it a surprise that they can both have the same properties? It is the particle nature of photons that allows Compton scattering to occur. 
Photons collide with electrons and scatter off of them as if they were both fast moving particles. This collision, as with all collisions, exchanges momentum and energy between the two particles. The photons have more of both, and so usually the photons lose momentum and energy and the electrons gain momentum and energy. This makes the electrons move faster (we think of this as being hotter). They collide with each other and with other particles, and this is what is holding up the interior of the Sun. But, if the electron gains momentum and energy, then the photon loses momentum and energy. A lower energy photon is one with a longer wavelength. So, the high energy gamma rays collide with electrons, become lower energy gamma rays, collide with more electrons, become X-rays, and so forth. As the photons work their way out from the center of the Sun, eventually, the conditions in the Sun become more gaslike, and the photons are finally absorbed by atoms, heating them up. This hot gas then rises to the surface of the Sun, where it radiates its energy off into space. That is how the energy finally gets out of the Sun. And that is how the Sun is held up against gravity!
If y’all are interested, I can go into more detail as to the fusion process some time later.
-Astroprof
(Sun image courtesy of NASA, SOHO)
A Ler…-- Rastos de Luz on October 8, 2006 at 8:03 am: 1
[…] “Holding the Sun up“, um post interessante no Astroprof sobre a geração da energia do Sol. […]
Andrew on October 8, 2006 at 8:55 am: 2
Forgive me if I sound stupid (perhaps I am) but,is 0.048x-27 the missing mass that you were refering to?.If you haven’t noticed,I tend to spend a lot of time on your site.HAHAHAHA,I guess it take a little more time for me to absorb exactly what it is that you are talking about!.I’m working on it!!!.
Visiting your blog has been a very educational experience….MORE PLEASE!!(hmmmm,why didn’t I feel that way in the 70’s and 80’s??.)
Andrew
Astroprof on October 8, 2006 at 11:12 am: 3
Andrew, yes, that is the missing mass. (I went back and realized that I had left out the word “missing” there, and I”ve put it it to clarify the point.). That is how much mass is converted to energy on each reaction. But there is an astronomical number of reactions going on every second, so it amounts to a total of about 4 million tons per second overall. Fortunately, the Sun is large enough for that rate to continue far into the future!
Thanks for the kind words! I appreciate them. I am glad someone is learning something from my little corner of the internet.
Tom on October 8, 2006 at 1:07 pm: 4
Great post!
Ben Davies on November 14, 2006 at 9:37 am: 5
I didn’t see that you answered the question you posed. Exactly where does the ‘missing mass’ that powers the sun come from?
Astroprof on November 14, 2006 at 9:57 am: 6
Ths “missing mass” comes from the hydrogen. A helium nucleus has less mass than four hydrogen nuclei. The difference in mass is converted into energy.
A deeper question would be why the more complex nucleus has less mass. You can think of this in terms of potential energy. Bringing the nucleons together in the helium nucleus results in lower potential energy from the strong force (much as bringing two masses together results in lower gravitational potential). Energy and mass are really different aspects of the same thing. So, the higher potential energy in the case of four separate hydrogen nuclei manifests itself as more mass.
Ben Davies on November 14, 2006 at 2:51 pm: 7
Hmm, I must not be looking at this right because that strikes me as an odd state of affairs. Potential energy has mass?
Would that be true of all potential energy - gravitational potential energy and electromagnetism for example?
Astroprof on November 14, 2006 at 4:02 pm: 8
Yes! All energy has mass. A moving object has more kinetic energy, so it has more mass than a stationary object. Thus, any system having more potential energy must also have more mass. Normally, this is a tiny effect, and hardly worth mentioning. But, the enormous potential energies of the nuclear forces result in a measurable difference in mass, as would extremely high velocities result in more mass (special relativity). In fact, this whole thing gets back to that darned relativity stuff and Einstein\’s famous equation: E=mc2 . But, that is what is at the heart of all this, and it is why it took so long before we understood how stars work.
Ben Davies on November 15, 2006 at 9:37 am: 9
OK, potential energy has mass.
What about Einstein’s famous thought experiment of the elevators?
If gravitational potential energy has mass, then in principle it seems very easy within the inertial system to make an experiment to measure differences in potential-energy-mass and thereby determine that I am in a gravitational field and not just being accelerated. I just weigh 2 masses when they are close together and again when they are apart.
That can’t be right.
Astroprof on November 15, 2006 at 10:58 am: 10
Hmm. A tough one.
But, you are sort of mixing special relativity and general relativity there. Still, if you are in the elevator with two bodies and measure them, you’ll get the same results no matter what. Remember that the relativistic effects act on the moving observer (or observer in a gravitational field) just as they do on the test subject. If you are outside the elevator making the measurements, then you’ve violated the basic assumptions of the thought experiment, so you can tell the difference.
If you just have one object in the elevator and are trying to measure it’s change in mass due to gravitational potential energy, you are doomed to failure because the potential energy isn’t really energy of the object (like we often misteach it in intro physics), but energy of the system, and if you aren’t looking at the whole system (including the thing outside the elevator making the gravitational field) then you won’t get the right answer.
Hmm. This is getting me to thinking that perhaps I should think of working up a relativity post or two.
Ben Davies on November 15, 2006 at 1:11 pm: 11
You can correct me if I am wrong, but I think this is a classical experiment done entirely within the inertial system. It doesn’t involve the ‘thing’ outside (the elevator) that is creating the field, except to make a test that can tell us what sort of field it is.
I have a balance beam with a mass on one side and 2 masses on the other side. I move the 2 masses apart and the measured mass goes up by the (mass equivalent) amount of the gravitational potential energy added by separating them.
This would contradict the equivalence principle of General Relativity: `there is no experiment a person could conduct in a small volume of space that would distinguish between a gravitational field and an equivalent uniform acceleration’
Are you sure that gravitational potential energy has mass?
Astroprof on November 15, 2006 at 1:40 pm: 12
Oh, I see. Yes, you would measure a different mass (or would if it were possible to measure a mass difference that small). It doesn’t contradict the equivalence principle, because the entire experiment is being conducted within the elevator. You’d measure a different mass (the same different mass) whether the elevator is accelerating or sitting in a gravitational field. The external field will have no impact on the experiment.
The equivalence principle applies to the environment of the elevator. You can’t tell if it is in a gravitational field or accelerating. That isn’t what this experiment measures. It measures the mass of the system of two particles, which does not depend upon the condition of the elevator.
Ben Davies on November 17, 2006 at 9:20 am: 13
Yep, I was looking at that one wrong. The gravitational attraction of my 2 masses is entirely within the inertial system.
So, would it be legitimate to try and estimate the mass of the gravitational potential energy between two galaxies using Newton’s equation of gravity along with Einstein’s equation m=E/(c*c)?
Astroprof on November 17, 2006 at 10:14 am: 14
I would imagine that you could estimate the gravitational potential energy mass between galaxies. But, galaxy masses are so difficult to come up with in the first place that the uncertainties in the galaxy masses would be larger than the energy mass. And, if you are thinking that this might be the source of the “dark matter,” well it isn’t. Already, cosmologists try to get estimates of the energy mass, and it doesn’t come anywhere close to what is needed.
Ben Davies on November 17, 2006 at 10:29 am: 15
I was just thinking of doing it for fun.
You could establish a lower limit by using a mass/luminosity relationship. Then assume that the 2 galaxies are point masses and that one sits still as the other one falls onto it. The kinetic energy at impact would be equal to the potential energy. Right?
To get a rough guess as to actual potential energy mass, you could throw in some estimate of non-luminous masses like white and brown dwarfs and gas clouds.
chris cooper on January 31, 2007 at 2:48 pm: 16
you cant hold the sun it is to hot and too big