“I don’t understand, profesora. The Sun’s fuel is hydrogen. The books say when the Sun runs out of fuel it will eject much hydrogen and collapse to a white dwarf. So it didn’t run out of fuel, yes?”

“That’s an excellent question, Maria. Your simple sketch of layered zones is adequate for a stable star like our Sun is now. When things go unstable we need to pay more attention to dynamic details like mass, pressure and diffusion. The numbers matter.”

“I had that the fusion zone is 30% up from the center, and the top of the radiation zone is at 70%.”

“Yes, but percentages of a straight line don’t really give us a feel for the volumes and masses. Volumes grow as the radius cubed. The Sun’s core, the part inside your 30% radius, holds (30%)³ which is less than 3% of the Sun’s volume. The convection shell on the outside is also 30% thick, but that zone accounts for ⅔ of the star’s volume.”

“But not ⅔ of the mass, I think. The core is the most dense, yes?”

“Truly. The core is <chuckle> at the core of the matter. It’s obviously under compression from all the mass above it, but there’s a subtler and more important reason. The Sun’s internal temperatures are so high that everything acts like an ideal gas, even near the center. Once you’re beneath the convection zone, the only transport mechanism is diffusion influenced by gravity. Helium nuclei weigh four times what hydrogen nuclei do. Helium and heavier things tend to sink toward the center, hydrogen tends to float upward. What effect does that have on the core’s composition?”

“The core is heavy with much helium, not as much hydrogen.”

“Good. Now, what’s next above the core?”

“The fusion zo– Oh! The place where there’s enough hydrogen to do the fusing.”

“If the temperature and pressure are right. That turns out to be a delicate balance. Too much heat makes that region expand, average distance between atoms increases and that slows down the fusion reaction. Too much pressure slows diffusion which then slows the reaction by hindering hydrogen’s entry and helium’s exit. Too little heat or too little pressure do the opposite. Now you know why the fusion zone is so narrow in our diagrams, only about 10% of a radius.”

“No fusion in the other layers?”

“Less than 1% of the total. So we’ve got nearly all the heat in the star coming from hydrogen‑to‑helium fusion in this diffusion‑controlled gaseous reaction zone buried deep in the star.”

“Ah! Now I see. It is wrong to say the star dies because it runs out of fuel. There is still much hydrogen in the upper zones, but the diffusion doesn’t let enough enter the fusion zone. That is why the fire goes out. What happens then?”

“It mostly depends on the star’s mass. Really big ones have a sequence of deeper, hotter fusion layers in their core, forming heavier and heavier atoms all the way down to iron. Each layer is diffusion‑limited, of course, and the whole thing is like a stack of Jenga blocks supported by heat coming from below. If reaction in any layer overruns its fuel delivery then it stops producing heat. The whole stack collapses violently to form a neutron star or a black hole. Nearby infalling atoms collide and radiate in an exponential heat‑up. But the stars are many millions of kilometers across. The outermost layers don’t have time to fall all the way in. Their imploding gases slam into gases exploding from the collapse zone — BLOOEY! — there’s a nova spewing hydrogen and stardust across the Universe.”

“That is how our Sun will die?”

“No, it’s too small for such violence so it’s fated for a gentler old age. Five billion years from now its core will be mostly carbon and oxygen. Fuel delivery won’t be able to sustain further fusion reactions. The radiation and convection layers will simply settle inward, releasing enough gravitational potential energy to start hydrogen fusion in an expanding cool red shell outside the core.”

“Hee-hee — no lo va la nova, profesora, the nova doesn’t go.“

• Thanks to Victoria, who asked the question.

~~ Rich Olcott

“Excuse me, profesora, you wanted me to come to your office?”

“Yes, Maria. Come in, please. I wanted to have a chat with you before you give your class presentation tomorrow.”

“I am a little nervous about it.”

“I thought you might be. I wanted to help with that. I’ll start by saying that your English language skills have gotten much better than you give yourself credit for. Better yet, you’ll be speaking before friends who want you to succeed. I’m sure you’ll do fine. I think if we go over your material together you’ll be more confident. Come open your laptop on my desk where we can both see it. Now bring up your first slide.”

“Yes, profesora. Already you know that the title of my presentation is ‘The Structure of The Sun.’ I only have one slide, this one, that shows a slice of a star like our Sun.”

“How did the star get that way?”

“It condensed from a galactic gas cloud that was mostly hydrogen. I plan to talk about that with waving of the hands because a good picture of it needs to be in motion and I don’t know how to do that yet.”

“Fair enough, just don’t skip over it. Beginnings are important. Now talk me through your diagram.”

“It starts in the middle ¿see the fusion zone? where protons, that’s hydrogen atoms without their electrons, are squeezed together to release energy and make alpha particles, that’s helium atoms without their electrons. The protons have the same charge so they push each other away, but they are beneath many kilometers of mass that push them together. Also, the temperature is very hot, tens of millions of degrees. Hot atoms move fast, so when the protons are pushed together it happens with enough force and speed .. sorry, I need a word, superar?”

“Overcome.”

“Thank you. The protons are pushed together with enough force and speed to overcome the charge barrier. The actual reactions are complicated. At the end there is an alpha particle, four times heavier than a proton, and there is much more energy than the overcoming used up. The fusion zone makes heat and the heavy alpha particles fall down into the ash zone. The heat must go somewhere. Already the center is hotter so the new heat goes upward into the radiation zone.”

“And it’s called that because…?”

“Because atom motion is so, mm, frantic?”

“Good word.”

“… So frantic that there’s no moving in the same direction together, no convection like when steam rises over boiling water. Heat can only travel by convection, conduction or radiation. If there is no convection, moving heat must go neighbor‑to‑neighbor by conduction which is collision or by radiation which is photons jumping between atoms again and again until they escape. I have read that one photon’s energy can take 10000 years to cross the radiation zone.”

“So how is the next zone different?”

“It is much higher up from the center, nearly ¾ of the way to the surface. The pressure is 100 times less than in the fusion zone. The atoms have more room to move around together and form winds to carry the heat up by convection. But they can’t only go up, they have to come down, too, and that’s why my drawing has loops.”

“Is there a name for the loops?”

“Oh, yes, they are called Bénard cells and they’re very much like what I see looking into a pot of water just before it boils.”

“What’s the orange above the convection zone?”

“That’s the part of the Sun that we see, the photosphere that emits light in a continuous spectrum. The Fraunhofer lines, the dark lines in the astronomer’s spectrum, are the shadows of atoms high in in the photosphere that absorb only certain colors. I was surprised to learn how narrow the photosphere is, not even 0.02% of the Sun’s radius. Anyway, that’s my presentation, but now I have a question. The Sun’s fuel is hydrogen. The books say when the Sun runs out of fuel it will eject much of its hydrogen mass and collapse to a white dwarf. So it didn’t run out of fuel, yes?”

~~ Rich Olcott