The End Of The Sun

The Helium Flash
The beginning of the end for a red giant the mass of our Sun occurs very suddenly.  As the helium "ashes" continue to pile up at its center, a higher fraction of them turn electron-degenerate.  It is an odd paradox:  even as the outer layers of a red giant star are expanding into a huge but tenuous cloud, its inner core is contracting down to form a buried white dwarf.  The temperature and pressure in the Sun's core will soar to 10 times their current values.  And roughly 1.2 billion years after it leaves the main sequence, at the height of its glory as a red giant, the center of the helium core of the Sun will become sufficiently massive, dense, and hot that something amazing will happen:  within a matter of minutes, it will ignite and burn.

When the temperature in the core reaches about 100 million degrees, the helium will begin to fuse into carbon by a reaction known as the triple-alpha process, because it converts three helium nuclei into one carbon atom.  This generates a great deal of heat.  However, unlike when the Sun was young and its core contained normal matter, adding more heat to the electron-degenerate helium does not cause it to expand and cool.  As I noted when I was discussing quantum mechanics, electron-degenerate matter behaves more like a liquid than a gas when you heat it:  its temperature swiftly rises, but it doesn't expand.  In other words, the self-regulating mechanism that keeps main-sequence stars so stable (hydrostatic equilibrium) is turned off in electron-degenerate matter.  If you add heat to a white dwarf, it just gets hotter.

As it happens, the triple-alpha process is exceptionally highly temperature dependent:  doubling the temperature of the reaction causes it to run roughly a trillion times faster!  So, as the fusing helium heats the core, which cannot expand to cool down, the increased temperature causes the helium fusion to suddenly proceed millions of times faster, which very rapidly heats the core even more, which in turn causes the helium to fuse way, way faster . . .

In short, the center of the helium core explodes.  About 6% of the electron-degenerate helium core, which by now weighs in at about 40% of a solar mass, is fused into carbon within a few minutes.  (This corresponds to burning roughly ten Earth masses of helium per second, if you are keeping score.)  For obvious reasons, astronomers call this the helium flash.  In roughly the time it takes to toast a bagel, the flash releases as much energy as our current Sun generates in 200 million years.  At the height of the flash, the Sun's core will very briefly equal the combined luminosity of all the stars in the Milky Way galaxy!  One might imagine that a conflagration of this magnitude would have a dramatic impact on the red giant – and it does, in a way, but not nearly so suddenly or violently as you might think.

This is because we tend to underestimate gravity.  Compared to the intimidating power of nuclear weaponry, the energy generated by dropping a few rocks doesn't seem very impressive.  But in fact, the gravitational energy of extremely dense, extremely large masses is startling – it is only our human prejudice, arising from the fact that we live on a puny pebble that is neither massive nor dense, which makes us think otherwise.

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Suppose we do take the Earth as an example of a large, dense object, even though it is about as dense as cotton candy when compared to a white dwarf.  To inflate the Earth to twice its size – that is, to lift the mass of the Earth against its own gravity until its radius is doubled – would require all the solar energy striking the surface of the Earth (a mere 185,000,000,000 megawatts) for the next 13 million years!

During the helium flash, a star's degenerate core is heated so intensely that it finally "vaporizes", so to speak.  That is, individual nuclei begin moving so fast that they can "boil away" and escape it.  The core reverts back into a (spectacularly dense) normal gas, and powerfully expands.  The enormous gravitational energy needed to expand 100,000 Earth masses out of degeneracy and up to several times their original volume is on a par with the energy release of the helium flash.  Or in other words, almost all the energy of the flash is absorbed by the titanic weight-lifting necessary to lift the core out of its white-dwarf condition.  Essentially none of the energy reaches the surface of the red giant, and indeed, if you were observing the red giant with your naked eye as its helium core flashed over, it is doubtful that you'd notice anything at all.

So, by human standards, the helium flash is a disappointing dud to watch.  By galactic standards, however, the red giant has been shot through the heart.  The sudden expansion of the core results in cooling so severe that it is something like the onset of an Ice Age.  The cooling immediately leads to much lower pressure in the hydrogen-burning shell that surrounds the core, and therefore to a calamitous drop in the energy output.  On a timescale which is almost instantaneous compared to the usual timescale that stars run on (perhaps as little as 10,000 years), the red giant's diameter and luminosity plummet to less than 2% of their former values.  For stars the mass of our Sun, the result of the helium flash is a collapse into an orangeish-yellow star with perhaps ten times the current solar diameter and 40 times the luminosity.  It is quite a comedown.

The End Of The Sun
The final 140 million years or so of the Sun's life will be very complicated.  After its collapse, as illustrated in Figure 1, the Sun will reestablish itself as a star with a double energy source:  it will have a dense (but not electron-degenerate) carbon-oxygen core surrounded by a shell where helium is burning into carbon, and outside of that it will have another shell where hydrogen is burning into helium.  (The core oxygen is created by slow fusion between carbon and helium at the core's surface.  In heavier stars, the oxygen can in turn fuse with the helium to make neon.)  Helium fusion produces only 9% as much energy per kilogram as hydrogen fusion, so energy-wise, the Sun continues to be mainly a hydrogen reactor.  90% of its luminosity still comes from burning hydrogen.

However, it is the helium surrounding the core which now dictates how the Sun will evolve.  The Sun more-or-less repeats what it did as a aging main-sequence star, except now with a carbon-helium mix in the core rather than a helium-hydrogen mix.  For a time it achieves relative stability and maintains hydrostatic equilibrium in its new incarnation as an orangeish-yellow "subgiant" star.  Thus, stars in this phase of their existence are sometimes said to be on the "helium main sequence".  From the fleeting perspective of a human lifetime, subgiant stars seem calm enough:  the well-known bright star Arcturus, whose light was used to open the 1933 Chicago World's Fair, is such a star.  It has not changed in any measurable way since the invention of the telescope.

But the high temperatures necessary to maintain helium burning mean that the Sun can only burn helium one way:  very fast.  The hot core dictates rapid hydrogen burning as well.  When it was on the normal main sequence, the Sun's luminosity held fairly close to 1.0 Lo for around nine billion years before brightening to about 2.7 Lo at the end.  On the helium main sequence, the Sun's luminosity will hold at about 45 Lo before brightening to about 110 Lo at the end.  Not so impressive as a red giant, but very bright nonetheless.

To maintain its subgiant lifestyle the Sun must tear through the fuel in its helium core 100 times faster than it did with its original hydrogen core.  After only a hundred million years on the helium main sequence, the Sun will once again begin to climb towards the realm of the red giants, and for the same reasons as it did before.  But there is no "carbon flash" equivalent of the helium flash that stopped the Sun the first time.  The temperature and pressure needed to ignite carbon-carbon fusion is too great for the Sun to achieve no matter how compressed its core becomes, so the carbon just accumulates and becomes ever denser.  The trend that the Sun showed on its first run as a red giant, when its core was crushed to white dwarf densities even as the outer layers billowed to tens of millions of kilometers in diameter, is unstoppable now.  The Sun becomes a red giant again, this time with a peak luminosity above 3,000 Lo.  Its outer layers blow further and further outward, beyond the orbit of Jupiter, even as its electron-degenerate core swiftly grows more massive and therefore smaller and more dense.

And eventually the day comes when the two part company.  The final days of a star are extremely complicated, because the helium-burning and hydrogen-burning shells don't burn at the same rate.  The hotter, faster-burning helium shell tends to race outwards and overtake the hydrogen-burning shell, and when that happens there is no more helium left to burn, so the helium shell fizzles out.  But the giant star quickly cooks up more helium, which then collects on the white-dwarf core until it suddenly flares up in a run-away helium ignition that is something like a baby version of a helium core flash.  The helium flare-up disrupts (turns off) the hydrogen burning for a short time, and so it goes.  At the very end, the Sun will literally cough itself to death as multiple fuel ignitions and choked-off fusion extinguishments rip through its atmosphere.

In four or five huge bursts, spaced roughly 100,000 years apart, the outer layers of the Sun will separate from the core and be completely blown away.  They will form an enormous, expanding shell around the solar system, and move outward to rejoin the interstellar gas.  Roughly 45% of the Sun's mass will escape in this way.  The remaining 55% of the Sun's mass is soon compressed into the white-hot, ultra-dense core.  To someone watching the Sun from far away, the Sun would appear to rapidly shift colors from red to white as the gaseous veil surrounding it is lifted.  (By "rapidly", of course, I mean a time span only a few times longer than the age of the pyramids.)

The exposed surface of the searing solar core will be so hot, at least 170,000 K°, that it will emit more x-rays than visible light.  (Post-red-giant stars are the hottest stars known, excepting neutron stars.)  Its luminosity will be a brilliant 4,000 Lo.  The Sun will have become a radiation source of truly galactic stature, its energy lighting up the escaping gas around it like a huge neon sign.  Such clouds are called planetary nebula, a misleading name, because 18th-century astronomers could barely see them with the telescopes of the time and thought that they looked like planets.  They are among the most beautiful sights in astronomy.  The photograph at right, of the nebula known as NGC 6751, is of one of my favorites.  The bright spot in the center is the post-red-giant parent star.

Remarkably, there is a star right at the point of blowing off its outer layers which can be seen with the naked eye.  This is Mira, the "Amazing One", so named by Arabian astronomers in the Middle Ages because Mira rather erratically varies over a span of roughly 330 days from being the brightest star in its constellation (Cetus, the Whale) to total invisibility.  Mira is the only classically named star that you cannot see, much of the time.  Modern instruments reveal that Mira is a vastly over-extended bag of deep-red gas that is not even closely spherical and which, at 2,000 K°, is also one of the coolest stars known.  Its atmosphere is undergoing complex undulations and oscillations as the nuclear burning below it sputters and gasps.  Hence, its variability.  In a paltry 500,000 years or less, Mira will be a planetary nebula.

As for the Sun, without its outer layers to supply it with more hydrogen, it can only maintain the gorgeous display of its nebula for a few thousand years, hardly more than a snap of the fingers by galactic standards.  The last dregs of fuel on the dense core will finally burn out, and for the first time in over twelve billion years the Sun will cease to produce energy.  The nebula will disperse and fade.  The Sun has become a white dwarf, little larger than
the Earth but 200,000 times more massive, and for billions of years to come all it will do is slowly cool off.

Due to their immense density, the time it takes white dwarfs to cool off is so great that not even the oldest known (nearly 12 billion years) have had time to cool much below 5000 K°.  These very old "white dwarfs" could perhaps more accurately be called "yellowish-white" dwarfs, but in any case, the Milky Way does not contain any "black dwarfs".  All of the ten billion or so white dwarf stars that our galaxy has produced since the Big Bang are still shining, however dimly.

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