Sunshine 2: the Sequel

By Eric M. Jones

LAST MONTH, WE ENDED WITH Arthur Eddington’s revolutionary theory that the Sun and stars were powered by atomic fusion, not fission. Hans Bethe finalized this theory in 1938 with a brilliant (nearly complete) description of the process. The modern age of astrophysics was born.

To a physicist, “temperature” is only a measure of how frequently particles, molecules, or atoms run into each other, and with how much kinetic energy. The Kelvin-Helmholtz theory of gravitational compression was exactly right when it said that things got hotter when compressed in a gravitational field, such as the center of a planet or star. But they were missing the key pieces needed to show how the Sun shines, because radioactive fission and fusion were unknown.

It is not some kind of strange energy that initially heats up material in the center of what will become a star, but only motion of the material that adds kinetic energy to the mix. Richard Feynman uses the example of gas molecules inside a piston and cylinder (for example, a bicycle pump). Each molecule of the gas inside the cylinder starts with a certain average velocity. When the piston pushes down on the gas, the velocity of the piston is added to the each gas molecule that touches the face of the piston; exactly like a Ping-Pong ball gets more velocity from touching a moving paddle. Very fundamental stuff.

After the initial Kelvin-Helmholtz compression heating, the star’s core is “supported” by the pressure created by thermonuclear reactions between light elements, usually hydrogen and helium. Or more succinctly, ionized hydrogen (protons) and ionized helium (alpha particles). This is where quantum chemistry parts company with standard chemistry.

Stars exist because the thermal energy in the core expands the star to balance the pressure of the gravitational force that is trying to crush the star into a dimensionless point. This is a very stable balance as long as the star has elements of atomic weight less than iron to use as fuel. In our middle-aged Sun, the balance will last for another five billion years, more or less as it presently appears.

So in the core of a star like ours, where the temperature and the density is very high, (a bazillion* degrees and ~150 g/cm3  or 8× the density of depleted uranium used to destroy military tanks) ionized hydrogen atoms—again, which are completely indistinguishable from protons—hit each other with such kinetic energy that they overcome their mutual electrostatic repulsion, and they stick together by the Velcro-like gluons of the “strong nuclear force” (one of the four basic forces in the universe) ... although it’s not quite that simple. Sadly, it never is.

Although we’ll try to avoid math, physics and radiochemistry, it is important to look at the fundamental stellar energy equation of 4 Hydrogen = Helium + Energy. This says that four hydrogen atoms under the right cooking conditions grow into one regular helium atom. It gives a bonus of E which, emblazoned over mushroom clouds on t-shirts everywhere, proclaim is equal to mc2. There are some detailed intermediate steps of gamma rays, positrons, deuterium, and neutrinos ... that the casual reader needn’t care about ... and if you are studying nuclear physics shouldn’t use this article as a reference.

So let’s see:

This is the missing mass for a single reaction: 0.029 u is equal to (we’ll skip the math; you’re welcome) 43 nanojoules. This is roughly the kinetic energy of a falling snowflake, but it adds up. In our Sun, 600 billion kgs of hydrogen are being converted into helium every second (day and night ... hah, Eric is easily amused). This reaction releases a tremendous amount of energy. The conversion of hydrogen to helium is only one small step in fusion processes that involve all the atoms and every piece of these atoms up to oxygen (15O) in our Sun and even up to iron (26Fe) in really big stars.

Furthermore, although this hydrogen to helium energy production in stars like our Sun is responsible for most of the energy output, much larger stars, like Sirius, derive almost all of their power from the nuclear carbon-nitrogen-oxygen cycle. This stellar fusion cycle won Hans Bethe a Nobel prize in 1967. This cycle starts and ends with 12C. The carbon acts a catalyst, as it is completely unchanged. The amount of carbon increases because it forms from three simple helium nuclei, one more of which pops out as a product at the end of each cycle.

Make sure you study for the test on Tuesday. I’ll be in my office from three to four this afternoon if you need help.

   12C = (6 proton + 6 neutron)
   12C + proton --> 13N + photon
   13N = (7 proton + 6 neutron)
   13N --> 13C + antielectron + neutrino
   13C = (6 proton + 7 neutron)
   13C + proton --> 14N + photon
   14N = (7 proton + 7 neutron)
   14N + proton --> 15O + photon
   15O = (8 proton + 7 neutron)
   15O --> 15N + antielectron + neutrino
   15N = (7 proton + 8 neutron)
   15N + proton --> 12C + 4He

For very large stars, this C-N-O cycle can take billions of years; for smaller stars it can take centuries to minutes near the end of the star’s life.

What happens when the stellar nuclear chemistry converts atoms to heavier and heavier elements? Each step of the way, the conversion of lighter elements into heavier elements gives up some energy,** thereby cranking up the system to make more energy. But the closer the nuclear chemistry gets to iron, the less energy output results. Iron and heavier elements require energy for transmutation.

The accumulation of iron in the core of a star happens extremely rapidly in the last few moments of a star’s multi-billion-year life. This is because making iron is the last gasp of energy production which prevents the star’s gravity from crushing it. All elements heavier than iron are made when the star is finished burning its lighter elements and the balance between the thermal ballooning and the gravitational force begins to fail. The star’s core collapses and the temperature rises until the star explodes as a nova, supernova or hypernova.

There will be almost no thermonuclear-synthesized elements heavier than carbon and oxygen created by our own Sun. The tiny percentage found there now exist because our Sun is a “Population I” metal-rich star that was created from earlier stars after they went supernova and blasted heavy metals throughout the galaxy. Very old but metal-poor stars are called “Population II,” and the very first stars that were created after the Big Bang out of hydrogen and helium with virtually no metal at all are called “Population III” stars. “Metal” is what astronomers call elements heavier than helium, whether they are metals or not. Stars in any particular galaxy are usually somewhat similar in age and composition.

In about five billion more years our star will slowly run out of the hydrogen fuel in its core. The core will contract and thus heat up. This will make the star’s remaining hydrogen outside its core expand the Sun into a red giant, swallowing the inner planets. (Say goodbye.)***

But even with its red giant gas ball, the size of the core will be small, and it will eventually burn hydrogen only on its surface. The core will continue to shrink and get hotter until the helium nuclei become hot enough to begin fusing into carbon (12C—remember that’s three 4He nuclei). Then the aforementioned C-N-O cycle will burn with reasonable stability for about 100 million years. The helium is eventually burned only on the core’s surface. The core will get still smaller but many millions of degrees hotter. The Sun will then become a red supergiant.

When the helium is all used up, only the C-N-O cycle remains active, but it is harrowingly unstable and blows off layers of material and gases to form what is called planetary nebulae (from William Herschel, discoverer of Uranus, who thought these strange-looking nebulae were the birth of planets).

In only tens of thousands more years the Sun will become a small core of carbon and oxygen. This phase is called a “white dwarf.” It is hot, but not hot enough to kick off nuclear reactions. It’s been all used up. It will be about the diameter of Earth but still have about half the mass of the Sun. Over billions of years it will eventually cool, fade out, and become a “sort of black dwarf,” although these definitions are changing. Nevertheless, it will become as dense and as cold as it can possibly get. The Sun is not (and can’t ever become) massive enough to end its life in any spectacular way.

[Hubble image of planetary nebula NGC 6751, at right.]

A careful reader should wonder why so very much can be known about the interior of stars and their energy production. Clearly we know virtually nothing in comparison about the interior of the Earth under our own feet.

There is a simple reason: We have a sky chock-full of examples to study. Furthermore, we can study them with giant telescopes equipped with spectroscopes that define what is going on, at least in the outside parts that we can see. There are “sequences” that define what is going to happen to stars, depending on their luminosity and color. One way to represent these “sequences” is with a Hertzsprung Russell Diagram (HRD), created circa 1910 by Ejnar Hertzsprung and Henry Norris Russell.

Within the HRD, our Sun is now at the intersection of 1, and about 5778 K in what is called the “main sequence.” Any normal-matter star can be placed on this diagram. As it ages it will fall off the main sequence type and jump up to become a red giant, then a super red giant, then a white dwarf. Stars don’t travel along these paths, even though it looks like they should. They are more like in “neighborhoods.” When the star runs out of energy, it packs up and moves to a less expensive neighborhood. The “White Dwarf” neighborhood is Hoboland.

Black Holes

When one can no longer say what elements are in the core of the star, we enter the weird realm of Degenerate Matter. The core is no longer made of simple atoms surrounded by electrons in their orbits. There can be ordinary atomic matter on the surface, but deeper down the electron orbits have disappeared. The space between nuclei have been crushed to zero by gravity, and perhaps the protons and neutrons have been squashed to quark-matter.

Unlike our Sun, many larger stars experience tremendously complicated and energetic deaths. Usually they explode as novas, supernovas, or hypernovas (determined by the paths they take, their size, and their end states) and then they become magnetars, pulsars, quark stars, neutron stars, Gamma Ray Bursters (GRBs), quasars (actually mini-quasars), black holes, white holes, wormholes, white dwarfs, collapsars ... Quite a zoo! And each has many variants and subcategories. They can also evolve from one into another. Each of these is an entirely new field of physics in itself. Additional variants and species will be discovered by future astronomers.

We can’t examine all the wealth of strange phenomena here, but one with history worth looking at is the black holes:

The idea of a black hole may have possibly been first theorized by John Michell in a letter written to scientist Henry Cavendish in 1783:

“If the semi-diameter of a sphere of the same density as the Sun were to exceed that of the Sun in the proportion of 500 to one, a body falling from an infinite height towards it would have acquired, at its surface, greater velocity than that of light, and consequently supposing light to be attracted by the same force in proportion to its ... inertiae, with other bodies, all light emitted from such a body would be made to return towards it by its own proper gravity.” —John Michell

Now this was pre-relativity when objects accelerating under Newton’s laws were believed to have no speed limits and the velocity of light was thought to depend on who was observing it. Furthermore, this was before the properties of photons were understood. So Michell was off just a bit ... but his was an illuminating notion nonetheless. Non-relativistically (which is a fancy way of saying it’s just plain wrong), a photon achieving the speed of light by being pulled towards a dense mass would do something remarkable when it reached the speed of light ... it would vanish. (Not at any particular radius from the object, mind you.) Any light corpuscule coming from the dense object would decelerate and be sucked back in (perhaps at some radius we could predict). One wonders what Cavendish thought about this.

By the way, Cavendish probably suffered from Asperger syndrome, was pathologically afraid of human contact, never married, and had no close personal friends—men or women. He was even too shy to speak to his servants, communicating by notes. He had a private stairway built so he wouldn’t run into his servants or anyone else when entering his home. But brilliant ... yes, indeed. The famous “Cavendish Experiments” determined the mass of the Earth. Cavendish, in whose honor James Maxwell’s laboratories were named, was remembered for his extraordinarily careful and thorough experimental design. OK, yes, his relative, William Cavendish, 7th Duke of Devonshire, served as Chancellor of the University and donated money for the construction of Maxwell’s laboratory. But still!

In 1931, using the ideas of Special Relativity, Indian American mathematician and physicist Subrahmanyan Chandrasekhar calculated that a body of degenerate matter more than 1.4× the mass of the Sun has no stable solutions. No stable solutions? Well, at the end of its stellar evolution the mass vanishes into a black hole and its radius is, well, zero. Not almost zero ... exactly zero. Eddington, and even Albert Einstein, opposed his arguments for reasons that were probably based on his skin color and nationality, not science. What do those ignorant brown-skinned natives know anyway? But as time went on, the evidence was all on Chandrasekhar’s side. A black hole would certainly form. He won the Nobel prize for it in 1983.

Even though a black hole has no dimension at all, just like an electron—it has enormous mass, charge, and angular momentum—all physical properties which are “conserved” in making the black hole, or in fact, anything else. If its “core” could emit a particle—perhaps a photon—the particle would be unable to exit the black hole. It used be thought that the Schwarzschild radius defined the limit of where outgoing particles stopped, but there are no outgoing particles from the “core” at all. The Schwarzschild radius merely defines the “event horizon” where a particle on the outside, traveling at the speed of light, finds itself going nowhere fast.

The simplicity of a black hole is deceiving: it can “radiate”—Hawking radiation is formed spontaneously; or it can have one or two (!) photon spheres orbiting around it, frame-dragging space around it, spinning and shooting off giant jets of material (or mysteriously maybe just one!) at nearly the speed of light. Much is unknown and much more will be revealed.

In conclusion, there has been much nerd-speak about how long it takes a photon to escape from the core of the Sun, where it is first generated, and travel to the corona where it is released like a bird to fly to Earth. (Actually, almost none of them get to Earth because the Earth is so tiny.) This is what mathematicians call a random walk: in the core of the Sun, one photon immediately crashes into an atom which re-radiates it to fly off again. But it’s not the same photon at all. A photon is only the force carrier for electromagnetic energy. All sunlight is by definition weak gamma rays—they arise from the rearrangement of atomic nuclei. So wear sunblock. Furthermore, what it means for the core of the Sun to be “transparent” to photons needs to be examined carefully. The mental image of a glowing ball at the core might be a fantasy. 

*Bazillion in this case means 15,000,000° C.

**In the first step, two protons collide to produce deuterium, a positron, and a neutrino. In the second step, a proton collides with the deuterium to produce a helium-3 nucleus and a gamma ray. In the third step, two helium-3s collide to produce a normal helium-4 nucleus with the release of two protons. And around and around it goes.

***Take heart! Four billion years ago human ancestors were not yet even organic slime. There is no reason to think that five billion years from now we will even resemble humans—or even remember them.

Eric M. Jones is the Associate Editor of “Perihelion.” He is an engineer, designer, consultant, and entrepreneur, working in the experimental aircraft community, NASA, space transportation companies, and the International Space Station.