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Why do stars shine for so long?

by Roger Bourke White Jr., copyright June 2002

Stars are matter going through the transition from being a huge, diffuse gaseous cloud into becoming condensed matter, either a white dwarf star, a neutron star, or a black hole. During this transition, the matter goes through several phase changes, and these phase changes are what makes the process take so long. The process takes millions of years for a big star and billions of years for a small star.

In the Beginning

The universe started with the “Big Bang”. In the early life of the universe, the first picosecond or so, all matter and energy were uniformly mixed.  It was a very hot and very small place, and the universe was expanding rapidly, but ironically, with very little turbulence (swirling around). At first, the temperature was so hot and space so small that matter was a mix of the subatomic particles that make up matter as we know it, but don’t exist as distinct entities today -- quarks, leptons and bosons. As the universe expanded (it started out smaller than a proton) and cooled, those exotic particles quickly combined into the particles that make up our matter of today: mostly protons, electrons and neutrons. But the particle changing was not finished yet. The matter particles in that small hot universe would bang into each other so hard and be "zapped" by such powerful gamma rays that they would often change their identity. A particle that was a neutron would get whacked so hard by some other particle or a gamma ray that it would change into a proton, then get whacked again and change, and so on.

As the universe expanded, it cooled. As it cooled, the whacking got less vigorous, and after that first picosecond, it cooled so much that subatomic particles "froze" into what they would become for the rest of the universe's life, except for changes caused by conventional nuclear reactions. The matter of the universe became a mix of electrons, protons, and neutrons (neutrons that minutes later decayed into protons and electrons) and dark matter (about which we still know little). At the time of freezing, some nuclear particles stuck to each other to create elements heavier than hydrogen (which has just one particle in the nucleus). Nuclei of deuterium (two), tritium and helium 3 (three), helium 4 (four), and just a trace of lithium isotopes (six and seven) showed up in matter. (there is no five particle matter that is stable)

And that was it. For the next 300,000 years the universe expanded and cooled, but it remained a hot soup of plasma composed of hydrogen isotopes, helium isotopes, and a few lithium isotopes--all existing as raw nuclei--and lots of electrons floating around on their own.

The Difference to Radiation Between Plasma and Neutral Gas

Plasma is a gaseous mix of neutral and ionized atoms and electrons freed from the ionized atoms. Ionized atoms are atoms that have lost at least one electron. Radiation of all kinds interacts easily with free electrons and to a lesser extent with ions. Neutral atoms, on the other hand, are very fussy about what kinds of radiation they will interact with. For instance, a light photon can travel ten, twenty, even a hundred miles through atoms of oxygen and nitrogen on Earth without interacting. When they travel that far and then enter our eyes, we get an inspiring view of mountains.

In plasma you will never get a scenic view. Each time a photon passes a free electron it will "zap" the electron -- it will exchange energy and momentum with the electron. The photon will change direction and energy, and so will the electron. The photons and electrons will also zap the ions in the plasma soup. When there is a huge mix of photons, electrons, and ions, they will all zap each other, and each will move in what's called a "drunk-walk" fashion.

The effect of the drunk walking is to slow motion in any specific direction to a crawl. For example, the sun is a ball of plasma. At the core of the sun, new gamma rays are being created by nuclear fusion. If those gamma rays were light rays and were being created in a neutral gas instead of plasma, they could reach Earth in about eight minutes, and they would still be the same light photons that they were when created. But in the real sun, the photons are gamma rays being created in a plasma, not a neutral gas. Because they are being created in the sun's plasma, they drunk walk their way to the surface, and they take about a thousand years to do it. During their journey they undergo countless zappings, and most change into light photons and ultraviolet photons by the time they reach the sun's surface. Part of the definition of what is the sun's surface--the chromosphere--is that above this layer light and ultraviolet photons can begin to move long distances without getting zapped. This means we can see that layer from earth. Below that layer we can't directly see what's happening because of all the zapping going on.

Plasmas trap radiation and force it to interact with matter. Likewise, the condition of matter in a plasma is quickly and heavily influenced by the photons that are trapped. The radiation will quickly wipe out differences in temperature and density in a plasma. Matter and photons are tightly bound in a plasma.

Meanwhile.. Back in the universe

For 300,000 years the universe was one big plasma ball that was getting bigger and bigger, and cooler and cooler. The matter and radiation in the universe were thoroughly mixed and very uniform in temperature and density. But change was coming -- big change.

First, the universe got cool enough for electrons to settle into stable orbits around helium nuclei, and the plasma consisted of protons and electrons banging around mixed with neutral helium atoms. The scattering of lithium atoms started picking up electrons, too, but not a complete set. It was a change, but the universe was still a plasma.

Then one day, the universe finally got cool enough for electrons to settle into orbits around hydrogen atoms as well and the universe suddenly became clear to light photons and those of less energy (infrared and radio waves). Light photons were free! They stopped interacting with matter at every nanosecond. They could now travel for years without changing energy or direction. Those photons that were of higher energy than light quickly banged around enough to lower their energy into the light spectrum, and they stopped interacting with matter as well.

Matter and radiation decoupled and that was a big change. That decoupled primordial radiation is still with us today as the cosmic background radiation.

The universe continued to expand and cool, and now that matter was decoupled from radiation, the matter could clump -- form differences in temperature and density. The gas of the universe could become hotter or cooler than average in different places, and become sparser or denser than average. The parts of the universal cloud that became denser and cooler at the same time started changing in interesting ways. Those parts became galaxies. (Dark matter had a hand in this process, too, but its role is not well understood.)

From Gas Cloud to Protostar

The first galaxies were simply places where the primordial gas cloud was denser and cooler. Where this happened, the gravitational well was slightly deeper than it was in the surrounding areas, so the surrounding gases started to move towards these places. Before, plasma had prevented this clumping, but now the tightly coupled radiation of a plasma was no longer there to prevent this from happening, so the gravity well got deeper and deeper as more and more gas came together, and the once very smooth universe became patchy. There were galaxies where gas was becoming dense (by standards of the universe of that day), and places that weren't galaxies became intergalactic space, where matter was less dense.

But the increased density of being part of a galaxy alone is not enough to make a star. Even today, there are some dark galaxies, which are huge clusters of gas that have very few stars.

In a world without plasma, another force resists a gas cloud collapsing. That force is simple pressure. As a cloud starts to collapse, the cloud's temperature and pressure will go up. If the gas is not ready to form a star, that rise in temperature and pressure will force the cloud to expand again, and nothing happens.

If a cloud is ready to form stars (and a single cloud usually forms dozens-to-millions of stars at roughly the same time), something will hold that gas cloud together long enough for it to cool a bit while the pressure remains high. Once the cloud cools a bit, the deepening of the gravity well will then power continued collapse of the cloud. (What triggers the initial collapses into star making clouds is not well known, but dark matter is likely to be involved. Once stars start forming in a cloud, the pushing around caused by supernova explosions coming from the first generation stars becomes an important factor and speeds up the star making process.)

This star making cloud continues to collapse, and as it collapses, the gravity well it is creating deepens. As the gravity well deepens, the gas atoms in the cloud gain potential energy. When they fall into the gravity well, they transform this potential energy into kinetic energy -- they start moving faster. As they move faster and bump into other atoms, they transform this kinetic energy into thermal energy, and the cloud gets hotter.

When the cloud gets hotter, its pressure rises, and it resists shrinking further, as discussed earlier. It would stop entirely except that when the cloud is hotter than its surroundings, it can cool off by radiating photons, mostly infrared photons.

When the cloud is big and only a little warmer than its surroundings, it takes a long time to lose excess heat by radiating photons, but as the cloud gets warmer and warmer, this process speeds up. It speeds up as the fourth power of the temperature difference. When the cloud gets hot, this process gets nice and quick, and this is why many stars will form from a single collapsing cloud. The "hot spots" within the cloud start collapsing more quickly than the surrounding cloud.  That collapse deepens the gravity well at the hot spot, so the pressure the hot spot can sustain is higher. When the pressure is higher, the temperature is higher, and the hot spot can cool more quickly. It's a positive feedback loop.

The Positive Feedback Loop

The gas cloud is collapsing because energy is being released as the process happens. The energy is gravitational potential energy, being transformed into kinetic energy, and then into heat, which is being radiated off.

This process of a huge diffuse cloud collapsing into specks of condensed matter that live in deep, deep gravity wells would be over in a cosmic eye blink if it weren't that another energy source besides gravity also becomes involved, and that energy is nuclear energy.

The cloud is in equilibrium as it collapses. It can't collapse faster than it does because of resisting gas pressure. It is only when the gas cools that the cloud can compress more.

The cloud is cooling, in the sense that it is loosing energy, but its temperature is actually going up as it collapses. The gravitational well is like a spring, squeezing the atoms together, and the temperature and pressure are counter springs, holding the atoms apart.

As the cloud collapses, the gravity spring gets stronger and stronger, so the temperature and pressure counter springs have to get stronger and stronger, as well.

Eventually, the temperature in the core of the cloud rises so high that hydrogen is once again being ionized -- plasma is back, and the photons have to start drunk walking again to get out. This slows the cooling process slightly, but not much, and the temperature continues to rise.

Then the core gets hot enough that protons start smashing into other protons so hard that when they collide one of them turns into a neutron, and they stick together and become an atom of deuterium. The deuterium quickly adds another proton to make helium three, and the helium three quickly adds another proton-transformed-into-a-neutron to make helium 4. Each of these processes releases a lot of nuclear energy. Helium 4 is stable at these temperatures -- protons and neutrons don't stick to it -- so the nuclear fusion process transforms hydrogen into helium, then stops.

Remember that our cloud is in equilibrium: It collapses as it cools. Well, when nuclear energy starts being produced, the cloud stops getting cooler, and it stops collapsing ... a star is born! A star is a gas cloud temporarily pausing in its collapse. The pause is caused by nuclear power keeping the core temperature up.

Enter the Phase Change

The process of transforming hydrogen into helium is a phase change. In this way, it is similar to melting ice or boiling water. When a phase change is taking place, the temperature where the phase change is taking place is held constant. In the case of ice melting, the temperature is held at 0 Celsius until all the ice melts. In the case of water boiling, the temperature is held at 100 Celsius until all the water boils off. In the case of a star core, the temperature is held at millions of degrees Celsius until all the hydrogen is converted into helium, and this can take a while.

The smaller a star is, the longer it will live. This is because the star's core pressure is low, and only a little nuclear heating is needed to keep the collapse in check. Some of the small red dwarf stars we see today have been burning since the first wave of star formation in the Milky Way, some 13 billion years ago. (If a cloud is too small, it will never collapse completely, so no nuclear energy is needed to prevent the collapse. This small chunk of gas cloud becomes either a gas giant planet, such as Jupiter, or a brown dwarf star which is about a thousand times bigger, but otherwise much like Jupiter.)

Bigger stars have higher pressures and higher temperatures in their cores. These higher temperature cores are trying to cool rapidly, so lots of nuclear energy is necessary to keep the equilibrium. The sun, a medium-size star, a yellow dwarf, has been burning about 4.5 billion years, and the hydrogen in the core is about half used up.

The core of a big star, a blue giant, is really stoked so it's trying to cool really fast, and lots and lots of nuclear energy is needed. A blue giant will live only millions of years, not billions of years.

The "Nuclear Pause" Ends, The Collapse Continues

Finally, the core runs out of hydrogen. What happens next depends on the size of the star.

If the star is small, the core collapses some more. When it does, the layers of the star just outside the core heat up hot enough to start fusing hydrogen into helium, and the core is kept warm and in equilibrium from this outside heat. This is not nearly as efficient, so lots of extra heat is generated, and the outer layers of the star have to dispose of a lot more energy -- the dwarf star turns into a red giant. In a red giant, the outer layers of the star get so overheated that they start evaporating -- leaving the star entirely -- and the star gets surrounded by a cloud of gas, which is mislabeled a planetary nebula because early astronomers didn’t know what they were looking at when they saw one.

Finally, the outer layers of the star are either fused into helium, carbon, and oxygen, or evaporate off, and the star becomes a white dwarf. The star has little atmosphere, and it consists mostly of condensed matter, a form of ultra-dense helium, carbon, and oxygen in which the electrons are floating freely between all of the nuclei. The planetary nebula drifts off, and this white dwarf quietly cools into a black dwarf. The collapse is complete.

If a star is large, larger than 1.5 times the size of the sun, final collapse takes a different and more spectacular form.

If the star is big, the equilibrium temperature in the core is higher. When it gets high enough, the helium nuclei start bashing into each other hard enough to produce carbon and oxygen, and elements from lithium through fluorine start to be formed in the core -- mostly carbon, nitrogen, and oxygen. This new fusion doesn't generate nearly as much energy as the hydrogen-to-helium fusion, but it's enough to make the core pause in its collapse again.

Meanwhile, the hydrogen-to-helium fusion is also taking place in the layers outside the core, just like in smaller stars, so this star is also generating lots of extra energy and becoming a red giant -- a really giant-sized red giant!

Not long after it starts, compared with the total life of the star, the helium in the core is used up. The phase change is complete, and the core collapses some more. When it gets hotter, elements around silicon in the periodic table can be created, and there is another ... shorter ... pause. The final pause comes as elements around iron are being created in the core. This pause doesn't last long at all, even by human standards. Perhaps a few hundred years, perhaps just a few days.

The elements around iron are the most stable in the periodic table. Uranium, for instance, releases energy when the nucleus breaks up, not when it gets bigger.

When the core overheats the iron nuclei, the system snaps -- there is no more energy to be had from nuclear power, and the nuclear pause is over. In the core, iron nuclei suddenly fuse together into a huge mass of neutrons, and the collapse of the core is complete.

If the core is small, it becomes a neutron star; if it is big, relativity raises its time- and space-twisting head and the core becomes a black hole.

This final collapse takes about a microsecond, and this core often concentrates a lot of momentum in the process. The result: The core can be spinning quickly and can burst out of the star's center into the wild blue yonder, sort of like a BB being shot out of a balloon. This is a supernova.

The Supernova Story

The outer layers of the star don't partake in this final collapse of the core of a supernova. They have a different destiny. When the core collapses, many things happen: The core stops supporting the inner outer layers of the star, the core releases a huge flood of neutrinos, and the core may leave the center of the star, headed lickity-split for the world outside.

When the inner layers just outside the core lose support, they start to move in, and because this collapse is quick, they leave equilibrium. For a moment, they get hot -- really hot, hotter than they should get -- and the nuclear fusions going on in them produce a lot more energy than equilibrium would allow. This extra energy makes the inner layers rebound, and parts of the inner layers start to explode out at the same time they are collapsing in. It's all very chaotic.

This churning, collapsing, and exploding works its way throughout the remainder of the star, and all except the core blows up, ultimately creating a huge, hot cloud of gas. This cloud of gas contains the heavier elements that were created in the layers outside the core, and as this cloud keeps expanding and pushes up against other gas in the big star-forming cloud that the supernova star grew from, it can seed the formation of other stars, as described above.

Neutrinos and Supernovas

The blowing up part sounds simple enough, but in fact, there’s a mystery here. A few scientists who heard this theory said, “Wait! Wait!” and then explained their concern.

When the core collapses and the explosions start, this is all taking place in plasma, and what does plasma do to radiation? It forces radiation to "drunk walk" its way away from where it is created.

This caused scientists studying supernova a big problem. The problem was: How does this explosive force actually leave the inner star and get to the surface? Why isn't "news" of the core collapse and the explosion taking a thousand years to reach the surface? Remember, when the core is not collapsing, it takes a thousand years or so for a photon to move from the core to the surface.

There was a related problem: While the core collapses, it still has to be in equilibrium. If this collapse is taking place in a microsecond, how is "heat" being removed from the core so quickly?

The answer in both cases is neutrinos.

Neutrinos are matter's most standoffish particle. Once created, a neutrino usually has nothing to do with other matter. Neutrinos that are headed at Earth will often go right through the center, and come out the far side, without a single interaction with any of Earth's matter. Often, but not always. Once in a while, the neutrino will bounce off a particle and transfer some momentum.

Neutrinos are created in the core collapse, and it is neutrinos, not photons, that move the core's "heat" out of the core and into the outer layers.

Now, we are talking serious neutrino production here. Neutrinos in a microsecond have to carry off energy comparable to what photons have been carrying off from the core for the last thousand years of its existence.

This flow of neutrinos is so thick that, even though neutrinos don't interact much with other matter, they manage to significantly heat up all the outer layers of the star. The neutrinos don't have to drunk walk through plasma, so it is neutrinos that "carry the news" of the core's collapse to the outer layers and start them exploding.

Stars Are in a Phase Change

So, that's it. Stars shine a long time because they are matter in the middle of changing from being a big, thin cloud of gas into a small, dense chunk of collapsed matter. The process pauses at the star phase because nuclear power keeps the core warm and keeps it from collapsing further. If the star is big, the pause is short, and the pause ends with a spectacular supernova explosion. If the star is small, the pause lasts a long time and ends quietly with a white dwarf.

 

--The End--

 

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