Nuclear Fusion

1. To begin with, there was some Hydrogen gas spread out in a section of space where nothing else existed. Hydrogen is the very simplest of atoms, with only one electron circling a nucleus which only contains one proton. These incredibly tiny particles are too small to see, but they have "mass", which you can sort of think of as weight. Around 300 years ago, Isaac Newton realized that every mass, of whatever size, attracts every other mass with what he called gravitation. He even figured out an equation to describe the amount of this attraction, which we now call Universal Gravitation.

   In a second or an hour, those individual Hydrogen atoms would not attract each other very much, but they really would be microscopically closer together. But given a million years, or a hundred million years, they could be attracted together into a big glob. Depending on how much Hydrogen was originally in the cloud, this glob might have different total mass. In this discussion, we will variously consider several different size globs, which we will describe by comparing the total mass with that of the Sun. One will be 0.001 solar mass; another will be 0.1 solar mass; 1.0 solar mass; 10 solar masses; and 1,000 solar masses.

2. These globs of Hydrogen are all huge! And they have enormous total mass. Where your mass might be 50 kilograms (equivalent to 110 pounds), the Sun's mass is about 1,980,000,000,000,000,000,000,000,000,000 kilograms! Keep in mind that all those atoms of Hydrogen are still attracting each other by gravitation. The result is that they get squeezed together, especially near the middle. The pressure down in the middle really gets very high due to this squeezing from the gravitational attraction.

3. High pressures usually cause raised temperature in that area, (this is generally due to something called the Ideal Gas Law) especially if any such heat cannot easily escape. The result of this is that the very center of the glob can get REALLY hot, really, really hot! Millions of degrees hot, simply from the squeezing of such enormous amounts of Hydrogen gas! Really amazing, but well established by many scientific experiments.

4. By the way, all of these globs will have become VERY close to perfect spheres by then! Another result of Newton's gravitational equation is that, if there was a corner of a cube, or even a high mountain, gravitational attraction would quickly cause it to flatten out, because the glob is made of a fluid material, the gas Hydrogen. This is why, even though we have never actually seen the shape of any star except the Sun (because they are way too far away), we absolutely know that they are all pretty spherical, like balls. If they happen to spin pretty fast, the middle gets bulged out. Even something "solid" like the Earth has such an Equatorial Bulge. In the case of the Earth, it is around 13 miles (20 km) difference in radius, due to the Earth spinning (rotating) once a day, which makes the Earth slightly "flattened", by about one part in 280. The reason this has to eventually occur is a subject called isostasy. Staying with the Earth for a moment, isostasy calculations indicate that no mountain on the Earth could be much taller than Mount Everest, because gravitational (isostatic) effects would cause even the solid rock of a mountain to gradually collapse over a few thousand years. In any case, all stars must essentially be round!

5. The temperature that develops near the center of this huge glob of Hydrogen gas how becomes important. The definition of temperature is based on the average speed of the atoms which an object is made of. When you have a situation where Hydrogen gas is heated to millions of degrees, the electrons and the nuclei are moving incredibly fast, getting up near the speed of light, the fastest speed that can be!

6. Nuclear Physicists have demonstrated in many experiments (in machinery called accelerators) that if you make a Hydrogen nucleus (a proton) go fast enough, it won't just bounce off another Hydrogen nucleus if it runs into it. Instead, at that extremely high speed, the two "fuse" together into one new particle. A nearby electron usually quickly gets jammed in there too, and the result is a new type of material, a nucleus of an atom of Deuterium. An important aspect of this is that a huge amount of energy is released when this fusion occurs. Einstein first figured out why this happens. If you carefully measure the exact mass of the Hydrogen nucleus and the Deuterium nucleus, you might expect that the Deuterium should have exactly twice the mass of the Hydrogen. It turns out that it is close, but is not quite, and the Deuterium nucleus actually has a mass slightly less (by less than 1%) than the two Hydrogens. Einstein realized that some mass "disappears" when this fusion happens, and that mass has been converted into pure energy. Einstein basically said that mass and energy can be converted into each other, and that they are "equivalent" by E = m * c². Only a tiny amount of mass disappears, but the equivalent amount of energy is enormous! And if you have countless millions of these crashes occurring every second, a huge amount of new energy shows up.

   This added energy appears as light and heat, which heats up the Hydrogen in the center of the glob even more, which speeds up more Hydrogen atoms and causes more fusions. This is called a self-perpetuating or self-sustaining nuclear fusion reaction.

7. Before Einstein, no one could figure out how the Sun created as much energy as it does. For many decades before Einstein, the total energy production of the Sun was known. It's total mass was known, too (due to Newton's gravitational equation and the Earth circling it once every year). Scientists had long known that if the Sun was actually "burning", like if it was made out of coal, it would have used up all of its (coal) fuel in only a hundred years or so, and human history records several thousand years of human activities! So it was well accepted that the Sun could not actually be "burning". But no one had even a guess about what could make such a huge amount of energy for so long. When Einstein discovered the equivalence of mass and energy, it was quickly accepted that the fusion described above MUST be occurring in the center of the Sun.

   Notice, I said CENTER! The outer surface of the Sun, what we see, is not burning at all, and it is not creating any energy either. It is far too cool for that, only being around 6000°C or 11000°F. That's really hot to us, but nowhere near the millions of degrees necessary for fusion to occur. That fusion can therefore ONLY occur near the very center of the Sun (and every other star). The outside surface of the Sun (or any other star) ONLY seems bright to us because the super heat at the center of the star has to move outward to get away from the center, and so the surface is actually heated from below from that heat rising through the star! We can never actually see the nuclear fusion occurring in any star (because it can only occur near the very center of it) and the surface we see is not actually "on fire" or even producing any energy!

8. Now, we need to consider our various mass globs. The glob that had a total mass of 0.001 solar mass would get very hot due to the gravitational collapse, but not hot enough to start fusion in its center. The result would be an object resembling the planet Jupiter, which roughly has a mass of 0.001 solar mass.

   The glob that started with a total mass of 0.1 solar mass would create temperatures high enough to start nuclear fusion, which would then be self-sustaining, so this would result in a star. Interestingly, when this fusion starts, the extra heat starts to inspire faster and faster fusion reactions, because the hotter it gets, the more fusions will occur, right? Well, that would be true, and the (new) star would very soon go berserk and be in a runaway, uncontrolled fusion event, and the entire star would use up all of its Hydrogen on a matter of seconds or minutes! If this happened, we would see no stars in the sky!

   There is another effect which occurs. There is a phenomenon called Radiation Pressure. In any human experience, this pressure is so small that it can never be sensed or measured. But with the astounding amounts of energy created in the center of a star, this radiation pressure can be very strong. The effect is that this outward directed radiation pressure pushes outward on all the Hydrogen surrounding the area, and it makes more space available (by very slightly making the star a few feet larger in diameter). As this available space slightly increases, the inward directed gravitational collapse pressure gets a little less, which means the temperature can drop a little. This effect would them enable FEWER fusions to occur and so the star would start to slightly collapse!

   EVERY star therefore has both of these effects, the fact that additional heat given off from the fusions tend to make the center of the star hotter to increase the rate of fusion, and also the effect of radiation pressure which has the opposite effect. This 0.1 solar mass star would have established a situation of stability, where the two exactly equal each other, which then causes the star to create a moderate amount of radiation, but extremely evenly, and for an unbelievably long period of time! It is possible to calculate how much of the Hydrogen gets used up by such 0.1 solar mass stars, and in the 5 billion years that we know our Sun has existed, such stars would have used up less than 1% of their Hydrogen! They will be able to continue producing energy (including light) for at least another 500 billion years!

   Next, if we consider the Sun, a mass 1.0 solar mass star, we know that it has used up roughly half of its original Hydrogen in those 5 billion years. In another 5 billion years, it will run out of Hydrogen as a fuel source, and some interesting things may occur but it figures to then simply "go out" and gradually just cool off. After a while, the surface would get more orange and then red, and then (visibly) disappear, and eventually just be a dark ball of stuff! Note that the expected lifetime of the Sun if less than 1/100 that of a star that had 1/10 the mass. This is due to research done where hotter sources radiate energy far faster than you might first expect! If any source of radiation is doubled in (absolute) temperature then it radiates energy sixteen times as fast! This dependence is as the fourth power of the absolute temperature.

   Now, we have no direct way of knowing exactly how hot it is inside the center of any star, even the Sun. The (visible) outer surface of the Sun might be twice as hot, but does that also mean that the temperature of the center is also twice as hot? No one really knows for sure, but a general assumption is that it is hotter. There are some indirect ways of estimating how hot it must be, from the total radiative energy measured (and calculated) from a star and some assumptions based on the spectrum of the star and sometimes some other information.

   Now, for our next blob, the one with 10 solar masses, we still have a similar situation, where the initial gravitational collapse caused high enough central temperatures to start fusion reactions. In this case, the central temperature has that extra contribution due to gravitational pressure and so we assume that the central temperature must be higher. Then, the rate of energy production would be much higher than that by the Sun, say 1000 times as much. This would mean that such a 10 solar mass star would use up its Hydrogen in around 1/100 as long as the Sun will (remembering that there was 10 times as much Hydrogen to start with). Such a star would seem hotter and brighter (due to a hotter surface), but it would be likely to exist for only 1% as long as the Sun, maybe 50 million years, a rather short time in astronomical standards!

   Finally, we consider the blob that started with 1000 solar masses of Hydrogen gas. The gravitational collapse of this blob would create ferociously high temperatures. This would immediately start creating very large numbers of fusion reactions in its center. The speed of all this developing would not allow the gradual balancing of the temperature of that central region, where the outward radiation pressure eventually exactly matched the inward pressure of gravitational collapse. In this case, the high mass new star would be extremely unstable. It would also use up its Hydrogen fuel at incredible rates! Even if it could somehow remain stable, its total lifetime might only be ten or a hundred years, before all the Hydrogen would be used up. Such a situation seems very unlikely, because the Hydrogen cannot really move around inside the star fast enough to fuel such rapid consumption, another factor that suggests that it will be extremely unstable. Such extreme high mass stars (1000 solar mass) are thought to be so unstable that none could make it through an entire lifetime, even though such a lifetime would only be a few years!

   Instead, such high mass stars are believed to all manage to blow themselves apart, almost immediately. The result is that the Hydrogen mass would get blown apart (with fusion immediately stopping). That gas might then re-collapse together, and it could all happen again, OR it might have gotten blown far enough apart to eventually collapse into smaller blobs, to form less massive stars which are more stable. Another result could be that the Hydrogen gas simply wanders around out in space for very long times. Eventually, it would certainly get gravitationally pulled into some existing star, or some newly forming Hydrogen blob, or even some "dead" star that had already burned out, because all those things will always have gravitational attraction.

   In the discussions above, we referred several times to a necessary balance between outward radiation pressure and inward gravitationally caused pressure. All stars that last very long have these two balance AS AN AVERAGE OVER TIME (a static balance), but they can still have temporary (dynamic) imbalances. Say that a star briefly gets slightly overheated (due to a combination of extra fusion due to the higher temperature and to an increase in gravitational pressure due to a slight collapse (essentially a slight reduction in the size of the core and maybe the entire star). It might then take a minute, or an hour, or a year, of such excess radiation occurring in the center before the radiation pressure is able to push the surrounding Hydrogen away enough to let it again get a little cooler, where less fusion would then occur. This sequence of "pulsing" could therefore occur over and over and over. The result would be what we call a variable star, one where the amount of light we measure changes, greater and lesser. Nearly all such variable stars have relatively small amounts of such variability, and it seems that most stars have at least a tiny amount of such variability.

   Even the Sun shows evidence of a slight variability, on a number if time scales. There is an eleven-year (or more correctly, a twenty-two-year slight variability that is most obvious regarding sunspots, but there seem to be both longer-term and shorter-term variabilities in the Sun, too.

   Most of the observed stars which show variability of small amounts seem to have very consistent patterns, where a light-curve can be drawn (brightness versus time) which closely repeats itself. Several categories of such "stable" variable stars have been observed, which have different light-curve shapes or different timescales. There are also "irregular" variable stars, which do not show such repeatability of the light curve, either in brightness or in the time involved for an entire cycle. Such irregular variables tend to have much greater changes in brightness, and therefore total radiative output.

   It seems to me that this makes a lot of sense. Small (dynamic) fluctuations in the instantaneous balance between radiation pressure and gravitational collapse pressure might easily (and quickly) cause the opposite (and therefore stabilizing) effect, so a repeatable, short-term variable would result. When those perturbations are much larger (usually only in massive stars which have natural instabilities to start with) then the response figures to be less identical and so less predictable. This would then logically make for a longer-term irregular variable star, with far larger variations in brightness.

9. This all results in a rather small range of actual mass of actual stars. The 0.001 solar mass blob never got hot enough to start nuclear fusion, so never became visible. The 1000 solar mass blob had entirely different problems, being so unstable that it could not maintain the fusion that started in it for more than a few days or a few years before blowing itself apart (due to that outward acting radiation pressure). The result is that we believe that all actual stars we can see have masses relatively similar to that of our Sun, rarely outside the range of 0.01 to 100 solar mass.

10. Everything we have discussed so far involved using Hydrogen as the source material in fusion reactions. The theoretical way that this fusion proceeds, through a relatively straight sequence of three separate fusions, turns out not to be very efficient, in a statistical perspective, as it requires random Hydrogen protons to sequentially hit and fuse to an increasingly bigger target. But, eventually, four of the hydrogen atoms get fused together into a Helium atom, which turns out to be more stable at that 15 million degrees (Kelvin, or absolute) in the center of a star. During the lifetime of the star, then, the Hydrogen is gradually converted into Helium. In the case of the Sun, it appears that roughly half of the Hydrogen has been changed into Helium in the five billion years the Sun has existed. As a result, we believe that the Sun will continue fusing Hydrogen into Helium for around another 5 billion years.

    Notice that I am avoiding calling all this "burning". It seems that most people, even astrophysicists, refer to this as "burning" Hydrogen, but that is actually now what is happening. The definition of what we call burning describes a CHEMICAL REACTION called OXIDATION, where a fuel combines with oxygen to release some chemical energy. Fusion does not require any oxygen, or anything other than simple heat (very high speed), for pretty much anything to experience such nuclear fusion. Try to NOT call it "burning"!

11. Is this the end? The star uses up all of its Hydrogen fuel and then goes out, to gradually cool and disappear from sight? Well, yes, for LESS massive stars. In some cases, they can then collapse even further, after the outward radiation pressure weakens, and such stars could then become what is called a white dwarf. Such a star has actually consumed all of its fuel, but then it had enough mass to collapse into a rather small size, resembling that of the Earth and not the Sun which has more than a million times the volume. But all the mass is still there, so such a white dwarf has incredibly high density, where a piece the size of a grain of sand would weight as much as a car! In the process of this extreme collapse after using up all of its fuel, additional increase in the central temperature develops due to the same gravitational pressure, which is why a white dwarf still appears white even though it is not actually creating any new energy. It has a rather small surface area, so the total loss of energy is relatively low, so a white dwarf could remain a white dwarf for many millions of years. But eventually, it would dim, and then be referred to as a brown dwarf, and then go out completely which is called a black dwarf (but none has ever been discovered yet.)

12. The situation for the more massive stars is FAR more interesting! After the Hydrogen is used up, these stars also collapse due to the lack of outward radiation pressure supporting the outer layers. But the more massive stars collapse even more inside, and the gravitational collapse causes even higher internal temperatures, above 100 million degrees Kelvin. When this new higher temperature exists, a new process becomes possible. The Helium nuclei can now fuse together (in groups of three) to form Carbon atoms. When this happens, a sudden new burst of nuclear fusion energy exists, and so a strong radiation pressure again pushes outward. There are two main possibilities:

    If the total mass is relatively moderate, the expansion is relatively stable and the star then starts an entirely new phase of its existence, of now using Helium as fuel and creating Carbon atoms in the process. If the mass is really large, this sudden expansion is unstable, and the star essentially blows itself apart, in an event which might be called a "nova" or "supernova", depending on just how massive it was. An important thing to note is that this now sends a lot of Helium atoms off into space! And keep in mind that massive stars have relatively short lifetimes, so in just 10 million years or so, the neighborhood that had only had Hydrogen gas now has a combination of Hydrogen and Helium. Later star formation could then start off with a combination of Hydrogen and Helium, and not just Hydrogen.

13. Now, let's look at those Helium-fusion stars that do NOT blow themselves apart! After all the Helium gets used up, the outward radiation pressure again reduces, and so the gravitational attraction again causes a collapse. Again, depending on the exact amount of mass involved, this could simply stop all fusion and eventually disappear from view. However, the gravitational collapse could produce even higher central temperatures, as long as there is enough mass involved. If that new temperature is high enough, the Carbon atoms can then fuse together into still heavier elements. such as Magnesium, Argon and Chromium. This sort of repetitive burnout and collapse can keep providing higher and higher central temperatures in really massive stars, with some of those stars then becoming unstable and blowing themselves apart to spread these new elements across the Universe, and others staying together to collapse again to form even heavier elements.

Now, if such a star would just go out and fade away, none of those new atoms would go anywhere, as they would forever be trapped inside dead and dark stars. Fortunately (for us!), a lot of those stars then conveniently blow themselves to bits, which then sends all those elements out into space. As already mentioned with Helium, later globs would include such mixtures of elements in forming a "next generation" of stars. Since the really massive stars live such short lives, like 10 million years, these new atoms then have plenty of time to wander across the Universe to become part of some distant new star formation a billion years later.

It is generally thought that the Universe is around 15 billion years old, and the Sun is around 5 billion years old. At ten million years per generation, a LOT of massive stars might have lived and exploded before the Sun was even a twinkling in the eye! This explains why our Sun contains many elements, which we know from its spectrum.

It appears to be especially important that there is some Carbon in the Sun. Carbon nuclei can act as a catalyst in enabling the fusion of Hydrogen into Helium operate much more efficiently than when only Hydrogen is present, and after a series of fusions occur, there is a nuclear decay which results in a Carbon atom and a Helium atom. Since the Carbon was necessary, but is not "used up" in this process, only a very small amount of Carbon is actually necessary, and the Sun seems to have enough!

Conclusion

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago