Stellar Evolution For Large Stars

Red Dwarfs Everywhere
A casual glance at the main sequence on an H-R diagram (Figure 1 on the solar evolution page) might lead one to believe that stars are evenly distributed all along it, but this is not so.  Stars are formed when interstellar gas clouds collapse and fragment, and the truth is, small fragments are much more common than large ones.  Even when you do have a large fragment, the ragged shape and uneven dust distribution of most of them mean that they only contract as a single object for so long, then they too sub-fragment into smaller clouds.  (Hydrogen and helium radiate heat very inefficiently.  This is true for most gasses, which is why air is such a good insulator and is used in thermopane windows and the like.  Dust radiates heat much better, so the dusty parts of interstellar clouds can cool off and collapse more quickly.)  The Sun is in the middle of the H-R diagram and in this sense it is an "average" star.  But if one takes a census of all the stars in our galaxy, it turns out that most of them are red dwarfs with less than one-half of the Sun's mass, and less than 10% of its luminosity.  The Sun may have an "average" position on the H-R diagram, but it is brighter than about 90% of the stars in the Milky Way.  Little dim red stars are very common; everything else isn't.1

You would never know this by looking at the sky, however.  Virtually every star you can see with your naked eye is either a very young, hot, bright, massive star, or a medium-mass star in an advanced stage of evolution, whether giant or subgiant.  This is because they are bright and you can see them, not because they are numerous.  Little dim red stars are more common by far – but there is not one visible to the naked eye.  The red dwarf nearest to the Earth was not discovered until 1917.

Stars that are less massive or only a few times more massive than the Sun evolve like the Sun does.  There are differences in the details, but those don't concern us here.  What we are interested in is the stars that quite definitely do not evolve like the Sun:  those rare objects at the far upper end of the main sequence which have masses at least nine times the solar mass.  These stars constitute only about 0.3% of all stars, but as we shall see, they are important beyond their numbers.


Navigation Menu
Introduction
Matter Under Pressure
The Birth Of The Sun
The Sun's Evolution
The End Of The Sun
How Large Stars Evolve
Type II – The Other Supernova
After The Supernova


1 – Of the 140 main-sequence stars nearest Earth, only 6 are brighter than the Sun.  119 (85%) are less than 10% as bright as the Sun, and an incredible 102 (73%) are less than 1% as bright as the Sun.

Large stars do evolve like the Sun for the first part of their lives, with one difference.  Nuclear reactions are very temperature sensitive, so even slight increases in pressure and temperature lead to large increases in the rate of nuclear burning.  Sirius, the brightest star in Earth's night sky, is about 23 times more luminous than the Sun, but it is only twice as massive.  Really massive stars, those at 20 solar masses and beyond, can blaze away at 160,000 times the solar luminosity.  Simple arithmetic tells you that if you increase the fuel consumption (energy production) of a star by a factor of hundreds or thousands compared to the Sun, but only increase its mass by a modest amount, then it will run out of fuel hundreds of times faster than the Sun.

And that's exactly what happens.  The Sun will stay on the main sequence for over ten billion years.  The giants at the upper end of the main sequence stay on it for at most fifty million years, and some for less than five million.  (By contrast, the dim red embers at the bottom of the main sequence burn their fuel so slowly that some of them are expected to remain on the main sequence for trillions of years!  Our knowledge of how extremely small stars evolve after they leave the main sequence comes entirely from calculations, because the Universe is not nearly old enough for any of them to have actually left the main sequence.)

Except for the time issue, however, large stars evolve like the Sun until the point where the Sun undergoes the helium flash.  Large stars burn so hot that they can reach the temperature of helium fusion before the core starts to turn electron-degenerate.  Thus, helium burning in large stars takes place in normal matter that can expand and cool as the helium burns, so they do not experience the run-away "flash" that the Sun will.  Unlike the Sun, they smoothly glide downward in luminosity by only a modest amount as they take up the double-shell arrangement of a "helium main sequence" star (carbon core, helium-burning shell, hydrogen-burning shell).  They do not suffer a sudden, 98% collapse in their radius and luminosity as the Sun will.

Then, things begin to get complicated.

At this stage in their evolution, smaller stars like the Sun just expand until their outer atmosphere expands away, and all that is left behind is a white dwarf consisting mostly of carbon and oxygen.  (Such dwarfs are often called CO stars, for that reason.)  The Sun isn't massive enough to ignite carbon fusion.  But large stars are, and only a few million years after they ignite their helium, and while they are still well within their red giant phase, they ignite their carbon and slide into a triple-shell arrangement.

Carbon fuses into a mixture of oxygen, neon, and magnesium, so one might imagine that the end point of a large star could be a beautiful planetary nebula just like the Sun's, except with an ONM white dwarf (oxygen-neon-magnesium) lighting it up rather than a carbon-oxygen dwarf.  And in fact, ONM white dwarfs are known to exist – but they are fairly rare.  The particulars of nuclear physics are such that if a star is massive enough to fuse carbon (about five solar masses), then it is almost massive enough to fuse any nuclear fuel (about nine solar masses).  Thus, only the occasional star whose mass lies within the relatively narrow interval of five to nine solar masses can end up as an ONM white dwarf.2  The majority of carbon-fusing stars just rumble onward, fusing one element after another.
2 – Determining whether a white dwarf is CO or ONM is notoriously difficult, because most of them only show hydrogen or helium in their spectra in either case.  The problem is, the tremendous gravity at the surface of a white dwarf makes it as smooth as a cue ball.  Any paltry drops of unburnt fuel left over from its red giant days can slide over the surface of the dwarf like an oil slick on a ball bearing, and completely cover it with an "ocean" only a few feet deep.  Thus, all we can see from Earth is – hydrogen or helium.  Fortunately, about 20% of known dwarfs have surface layers so thin that the substrate can be seen anyway.

When a large star (mass > 9 solar) moves past helium fusion, its interior undergoes a rapid-fire series of ignitions of different nuclear fuels, each burning in its own shell.  In less than 10,000 years, the star moves from a double-shell arrangement like the Sun will have to a bewildering multi-shell structure like an onion.  The details aren't critical to our discussion, but a summary of what the large star's interior looks like near the end is amusing (see Table I).

Table I – The Shell Structure of a Large Star            

Shell (or Layer)Main Element What It Is Doing
Surfacehydrogennothing
First Shellhydrogenburning to helium
Second Shellheliumburning to carbon
Third Shellcarbonburning to oxygen, neon, magnesium
Fourth Shellneonburning to oxygen, magnesium
Fifth Shelloxygenburning to sulfur, silicon
Sixth Shellmagnesiumburning to sulfur, silicon
Seventh Shellsiliconburning to iron
Coreironnothing

Each shell in the star burns much more rapidly than the one above it, primarily because it is burning at a higher temperature.  Yet, because the energy yield from nuclear fusion goes down as the mass of the nuclei go up, the shells provide progressively less and less energy until finally, when the massive red supergiant reaches iron, they stop generating energy altogether.  The problem for the supergiant at this point is not inadequate temperature and pressure in the core, as it was with the Sun and carbon fusion.  The problem is that the red supergiant cannot fuse iron because iron cannot be fused.

I have noted previously that there are two ways to obtain nuclear energy:  by fusing light elements into heavier ones, or by fissioning heavy elements into lighter ones.  In other words, either way you move towards the center of the periodic table of the elements.  Common sense tells you that these trends have to meet somewhere, and they do:  at iron.  In the world of nuclear energy, iron lies in the lowest part of the lowest valley.  You must always add energy to an iron nucleus to climb out of the valley and change it into any other element.  In principle, any element below iron (iron is element #26) can be fused to liberate energy, and any element above it can be fissioned to liberate energy.  But iron itself cannot liberate energy:  it is the nuclear-energy equivalent of a slag pile.  The figure on the right is a graph of the "nuclear valley" that shows how much nuclear energy is potentially available from all of the elements.  Moving downward releases energy; moving upward requires that energy be added.

Thus, the iron core at the center of a red supergiant star is the end of the line.  Without a source of nuclear energy to maintain equilibrium, all the core can do is contract.  The silicon fusion in the seventh shell yields very little energy compared to other fusion processes, so the silicon shell must burn extremely rapidly to support the layers above it.  This, plus the voracious fuel expenditure of the red supergiant (by this stage, it can easily be 150,000 to 500,000 times as luminous as the Sun) causes the iron core to grow at a precipitous rate.  Within only a day or so(!) after the ignition of silicon burning, the iron core begins collapsing into an electron-degenerate state and effectively becomes an extremely swiftly growing white dwarf star at the center of a red supergiant star.  For a very short while the nuclear burning above it continues, but for a star as massive as this one there is not much time left before the burned-out iron "ashes" in the core grow into a ball 1.4 times as massive as the Sun.  As predicted by Chandrasekhar in 1931, the degenerate iron is then as massive as a white dwarf can be.

It has reached Chandrasekhar's Limit.

In the blink of an eye, the entire iron core collapses from the size of the planet Mars to a sphere only 12 miles across.  Under the fantastic pressure of the collapse, the iron nuclei are smashed so closely together that they are literally crushed out of existence and turn instead into a soup of swarming protons and neutrons.  At such densities the rules of quantum mechanics force the electrons to fuse with the protons (which converts the protons into neutrons), and in a raging instant, neutrons are almost all that is left.  The core of the red giant suddenly convulses into a bizarre, gargantuan "nucleus" with 1.4 solar masses of neutrons, very few protons, and a density of billions of tons per cubic inch.

The electromagnetic forces that had once held up the electron-degenerate matter in the white dwarf are gone, because there are no longer any electrons.  As the neutrons are crushed down to the density of atomic nuclei, however, the strong nuclear force comes into play.  The strong nuclear force doesn't like particles to get close together any more than the electromagnetic force does, and the strong nuclear force is, well, strong.  When it finally exerts inself, the collapsing neutron matter ringingly slams to an almost instantaneous halt at a radius of perhaps six miles.

Meanwhile, behind the neutron matter, normal matter from the layers just above the core is plunging downward with a gravitational acceleration so phenomenal that in the few tenths of a second it takes to reach the center, it is already moving at 25,000 miles per second.  A mass of sulfur, silicon, and oxygen that is a quarter-million times more massive than the Earth and moving at 15% the speed of light slams into the neutron core – and rebounds off it like a rubber ball hitting a solid steel bulk-head.  An enormous shock wave begins to spread outward.

The collapse of the white dwarf core into a neutron mass has released far more gravitational energy in the span of one second than the star has released in the form of nuclear energy in its entire life, and we are talking about a very large star.  (As I pointed out when discussing the helium flash of solar-type stars, it is flabbergasting how much energy there is in gravitational collapse, if the collapse is massive enough and deep enough.)  Almost all of this gravitational energy has been transformed into heat in the neutron core, but it does not stay there.  Almost as swiftly as it was created, the energy is radiated away by subatomic particles known as neutrinos.3  The details of what neutrinos are and how they behave is beyond the scope of this essay, so suffice to say that whenever a proton and an electron are fused into a neutron inside the star, the fusion will generate about ten neutrinos.  This is critically important because ordinary collapsed stars (that is, white dwarfs) cool off by emitting light, whereas a collapsed neutron core cools off mostly by emitting neutrinos.  And the difference is, it takes a white dwarf billions of years to radiate away its heat, but it takes the neutron core only about 10 seconds.

The gravitational collapse of the core thus releases a torrent of some 1058 neutrinos, each carrying approximately the same kinetic energy as an electron in a 10-million-volt lightning strike.  It is almost impossible to grasp how much energy this represents, so I will just describe what happens to the red supergiant star next:

About 99.7% of the neutrinos punch through the outer layers of the red giant as though they aren't there, and race into space at the speed of light.  (Stopping a neutrino with ordinary matter is about like stopping a rifle bullet with a bowl of Jello – which is exactly why the neutrinos radiate away from the neutron core so readily.)  The remaining 0.3% of the neutrino pulse is absorbed by the very dense matter in the shock wave retreating from the center.  An absorption of 0.3% might not sound like much, but 0.3% of an unimaginable quantity is still unimaginable.  The shock wave is instantly blasted into a super-heated maelstrom so hot, the resulting detonation literally blows away everything above the neutron core.  At least five solar masses of gas, and possibly four times that much, are hurled away from the star at velocities of tens of thousands of kilometers per second.  The energy of the ejected gas is so great, if it slams into a nearby interstellar cloud it can shock the entire cloud into a sudden collapse, thus creating scores of new stars at a single blow.









3 – Taken from the Italian for "little neutral one", neutrinos are subatomic particles whose mass is probably less than one two-millionth that of the electron, which means that the slightest smidgeon of energy is enough to propel them to nearly the speed of light.  They are produced in vast numbers by nuclear reactions:  in the time it has taken you to read this sentence, about 1012 neutrinos have passed through your body, courtesy of the Sun.  Neutrinos are electrically neutral.  Combined with their speed and size, this means that their penetrating power is phenomenal.  Less than one in a trillion which impacts the Earth is stopped:  the rest pass completely through the entire planet as if it wasn't there, and keep going.  Neutrinos are detected by using vast detectors and sensitive instruments, and patiently waiting for the occasional "strike".

For a few months, the incandescent glow of the remnants of the former red supergiant is a hundred billion times as luminous as the Sun.  For a few months, it is nearly as bright as all the rest of the stars in the galaxy combined.  Even six months later, it can still be a hundred million times brighter than the Sun.  Yet, even this brilliant light represents only a percent or so of the energy in the ejected gas, which itself contained less than a percent of the energy generated by the neutrino pulse that signaled the final core collapse.  If by some awful mechanism all the energy in a core collapse could be turned into light, then even an explosion 500 light-years from Earth would roast us under heat and light brighter than the Sun's.  A star that experiences such an explosion is called a supernova.  These explosions are rare:  there has not been a visible supernova in the Milky Way since 1604.  (Luckily, since supernovas are so bright, it is easy to observe them in other galaxies.)

Figure 1   The Crab Nebula
In the aftermath of the explosion, the neutron core is left naked and alone in space.  Hence astronomers call it a neutron star.  A bit of matter is usually ripped off its surface by the supernova explosion, so neutron stars usually have a mass about 1.3 times that of the Sun.  Normally they emerge with a rotation of at least 10 times per second, and possess magnetic fields a trillion times as strong as Earth's.  Such a field, combined with their dynamo-like rotation rate, means that a newborn neutron star is something like a giant particle accelerator.  Electrons caught in the whirling magnetic fields are accelerated nearly to the speed of light and beamed away.  Whopping amounts of radiation pour out of the new neutron star, lighting up the fleeing gases from its former red-giant life in much the same way that lesser stars light up planetary nebula.  The light show doesn't last too long by galactic standards:  the only source of energy available to the neutron star is its rotation, and even though a flywheel 12 miles across and weighing in at 430,000 times the mass of the Earth is a formidable flywheel, it still must run down.  It takes about 25,000 years.

The most prominent neutron star as seen from Earth is the one at the center of the Crab Nebula, shown in Figure 1.  This nebula is expanding so swiftly that small differences between this photo and photos taken only 60 years ago can be seen with the unaided eye.  The Crab Nebula is the aftermath of a supernova that exploded in 1054 AD.  (Well, to be precise, the light from the explosion reached Earth in 1054 AD.  The star itself exploded some 6000 years before that.)  This supernova was so bright it could be seen during the day, and it was observed and recorded by everyone from the Navaho to the Chinese.

The neutron star at the center of the Crab Nebula rotates about 30 times per second.  In the late 1960's it was one of the first so-called "pulsars" to be identified.  Pulsars are rapidly rotating neutron stars that have magnetic hot spots on their surface which send out beams of radiation something like the beacon on a lighthouse.  As the beam flicks across the Earth, the neutron star appears to emit a sudden pulse of radio waves, hence the name.  Due to a neutron star's immense rotational inertia, pulsars blink with a precision that rivals that of an atomic clock.  When pulsars were first detected, astronomers were so uncertain whether any natural phenomena could produce such precision timing that they only half-jokingly christened the pulsars as LGM-1, LGM-2, etc.  The LGM stood for Little Green Men, because they had doubts that anything except an advanced civilization could produce such a beacon.

To the great frustration of astronomers, there has not been a visible supernova close to the Earth since the advent of space-based telescopes.  The supernova known as SN 1987a is, at about 180,000 light years, the closest so far.  A new supernove as close as that which made the Crab Nebula would send astronomers stampeding to the nearest observatory so swiftly, there is little doubt that a few junior Fellows would end up on the floor with footprints on their backs . . .


Next:  Type II – The Other Supernova