How the Sun works, from the inside out

“…it is reasonable to hope that in the not too distant future we shall be competent to understand so simple a thing as a star.” –Arthur Eddington, 1926

(For Mike H., who wanted to know.)

The Sun — like nearly all stars — burns bright through its nuclear reactions, sending light, heat and energy out into the Universe over a timespan of billions of years.

Image credit: NASA / ISS / Space Shuttle Atlantis.

But it didn’t need to be that way. With the mass of about 300,000 Earths, nearly all of it in the form of hydrogen fuel, you can just as easily imagine a huge nuclear explosion on the scale of an entire star, burning all of the Sun’s fuel up in a tiny fraction of the time.

Let’s take a look inside, and find out why the Sun takes billions of years to burn its fuel up. And let’s start by comparing the Sun with the rest of our neighbors: the planets in our Solar System.

Image credit: Jeff Root at freemars.org.

When you take a look at the inner planets, it’s no surprise that Mercury, the smallest planet, is also the least massive. Mars is next, followed by Venus and Earth, which are close in both mass and size. And this makes a whole lot of sense: you pile more and more atoms on top of one another, and where you’ve got more atoms, you get a larger and more massive object in the end. But at the heavy end, there’s a bit of a surprise.

Saturn — the second largest planet in our Solar System — is nearly the same size as Jupiter, with a diameter about 85% as large as its Jovian superior. But in terms of mass? Saturn has only one-third the mass of Jupiter! To understand what’s going on, we’ve got to go down to the atomic level.

Image credit: Engineering and Physical Sciences Research Council, retrieved from sciencebuzz.org.

There’s not some atomic catastrophe at play here, where Jupiter is made out of gold or some other incredibly dense element. Instead, Jupiter and Saturn are made out of nearly identical stuff, but Jupiter really has about three times as much of it as Saturn does.

The big difference is that Jupiter has so much mass that the atoms themselves start to compress one another at the center, packing them tighter and tighter together as more mass accumulates.

This has gotten really fascinating as we’ve discovered planets outside the Solar System, because as planets get much more massive than Jupiter, they start to get even smaller in size.

Image credit: F, Fressin et al., 2007, retrieved from oca.eu.

As you make your object more and more massive, it continues to shrink and shrink. By time your planet is about 13 times 70 times (thanks, Ned Wright) as massive as Jupiter — or about 8% as massive as the Sun — the hydrogen atoms at the core are so dense and under so much pressure that they can actually begin fusing together into heavier elements!

Image credit: Randy Russell, of the proton-proton chain fusion process.

And when that happens, your “too-big-to-be-a-planet” mass expands. When you were just a planet, gravity pulls inwards on all of your atoms, attempting to collapse them down to as small a space as possible, but the atoms themselves can resist it. But once you achieve too great a density at too high a pressure, and fusion starts, you begin turning mass into energy. And what does this energy — in the form of radiation — do?

It pushes outwards. Rather than atoms holding up a star against gravity, it’s now the radiation from the nuclear fusion you began. A low-mass star like a Red Dwarf is many times larger than Jupiter, while a star as massive as the Sun is significantly larger still.

Image credit: NASA and SeRgio.

And for our Sun, the energies we’re talking about are huge! Every single second, the Sun fuses six hundred million tonnes of hydrogen into helium! And while that gives us a huge amount of energy, remember that the Sun itself is also huge.

Image credit: NJK / Solar Navigator.

Those six hundred million tonnes of hydrogen that get fused every second happen in the Sun’s core: the innermost 20% of the Sun (by radius). But remember that the Sun is 700,000 km in radius; you could line up more than 100 Earths across its diameter! If you break it down by volume, you find that the Sun produces “only” about 300 Watts per cubic meter, or the amount of body heat generated by two adult male humans.

(So yes, a crowd of humans the size of the Sun’s core could produce just as much heat as the Sun, in theory. That is, as long as you can keep them alive.)

This is probably very different than your conventional view of fusion, which likely takes a small “mass” like this…

…and turns it into a huge, many-mile-wide explosion, like this.

The rate of fusion is largely determined by the size of your star’s core. For our Sun, something like 99% of its fusion takes place in the innermost 24% of the star. For a lower-mass star, the core is progressively smaller and smaller, driving the rate of fusion down substantially.

Paradoxically, then, the lower your star is in terms of mass, the dimmer it is, the cooler and redder it is, and the longer-lived it is, too!

A G-type star like our Sun may live from 10-15 billion years, while a low-mass, dim red dwarf star (an M-star) may live anywhere from hundreds of billions to many trillions of years, far longer than the age of the Universe!

But on the other side, as you get more and more massive, your fusion-burning core gets progressively larger and larger. The largest, bluest O-stars weigh in at more than 100 times the mass of our Sun, and burn through their entire complement of hydrogen fuel in less than one million years!

Amazingly, for all hydrogen-burning stars like our Sun, the only major determinant for the star’s lifetime is its mass.

Image credit: SOHO / NASA / ESA.

So even though it might not look it, the reason the Sun burns its fuel at the rate it does is because this is the right rate for its mass. Given that nuclear fusion produces the radiation necessary to cancel out the Sun’s gravitational force throughout its interior, it’s this nuclear burning that keeps the Sun from either expanding or contracting. (Variable stars have missed this equilibrium mark, and expand due to too much radiation, then don’t produce enough radiation and contract, and then fuse more atoms together and expand again. Or maybe not.) The larger your star is, the more radiation is pushing out and the faster you’re burning through your fuel.

And that’s how the Sun works, from the inside out!