A Brilliant But Short Life

Stars at least 8 times the mass of the Sun are called high-mass stars.  These are the type O and B stars, and as we saw earlier, they live only a short time of order 10 million years on the Main Sequence.  Still, they go through very similar stages of their lives that we saw for the low mass stars.  Recall that these stages for low mass stars are:

• hydrogen burning in the core while on the Main Sequence
• when the hydrogen in the core is exhausted, the star begins hydrogen burning in a shell around the degenerate helium core while moving up the Red Giant Branch.
• as the hydrogen fuel runs out, extreme pressure raises the temperature to 100 million degrees, where helium burning becomes possible.  Suddenly, at the helium flash, the degenerate core starts burning helium and the star moves toward (but not quite to) the Main Sequence again.
• as the helium in the core is exhausted, the star begins helium burning in a shell around an inert carbon core while moving again up the H-R diagram to become a Red Supergiant.

Low mass stars end their lives here, by expelling their outer layers due to thermal pulses in a planetary nebula phase, but high mass stars have so much mass that they can survive this phase.  In our earlier analogy of a pressure cooker, high-mass stars have a heavy "lid," so they keep on cooking. We will treat that in a moment, but first let's look at how high mass stars differ from low mass stars in nuclear burning.  In low mass stars, the burning of hydrogen to helium in the Main Sequence stage happens in the slow, proton-proton reactions that we discussed earlier.  For high mass stars, there is a faster mechanism to convert hydrogen to helium, called the CNO cycle, but it requires a higher core temperature than occurs in a star like the Sun.  The CNO cycle uses carbon as a catalyst, in which carbon is used in the reaction, but in the end the carbon is returned to be used again.  Here is the reaction, step by step: The steps build a larger and larger nucleus, starting with carbon, then to oxygen, then to nitrogen (hence the name CNO), each time absorbing a proton, until in the end the nucleus splits into a helium nucleus and the original carbon.  So the carbon is not used up in the reaction, and survives to react again.  The net result is to combine four protons into a helium nucleus, just as the proton-proton chain does, but faster.

One of the consequences of this faster power generation is that more photons are produced.  Remember when we said that the dust tails of comets are swept away by light pressure from the Sun?  In a similar way, the photons produced in the CNO cycle are numerous enough to cause a significant pressure, called radiation pressure, that helps support the star against gravity.

During this stage, the star is burning hydrogen to helium in its core, and so it is sitting on the Main Sequence. Depending on its mass, it may live only 1-100 million years in this stage--much shorter than the Sun's lifetime.

Once the high mass star starts to run out of hydrogen in the core, and starts burning hydrogen in the shell, it expands into a Red Giant stage just like we saw for low mass stars.  But there is no helium flash.  The helium core is so hot that nuclear fusion begins there slowly over time, without degeneracy pressure becoming a factor.  The star slowly moves back toward the Main Sequence, and burns helium in its core, but the rate is so high that the star runs out of helium in just a 100,000 years or less.

Once the high mass star reaches the Red Supergiant stage, and is burning helium in a shell around the inert carbon core, the core can reach a high enough temperature (600 million K) for carbon to fuse into heavier elements!  This is different from the low-mass star case, where the temperature to fuse Carbon is never reached. But the carbon is exhausted in only a few hundred years, and the next stage of still heavier elements begins.  Each stage lasts a shorter and shorter time, partly because the reactions are less and less efficient -- each reaction produces less energy than the previous one.  The reactions can become quite complex inside the star, because as the inner core is producing energy from one type of reaction, an outer shell may be producing a lower temperature reaction (e.g. burning helium to carbon, or hydrogen to helium) until the central part of the star resembles an onion with several layers all going at once.

 

The simplest set of reactions are called helium capture reactions, where helium is captured by a series of more massive elements in the sequence carbon to oxygen to neon to magnesium.  Other reactions, which can take place only at the highest temperatures and pressures, are C + O -> Si, and Si + Si -> Fe.  Once silicon is fusing into iron, the game is up for the star.  No reaction with iron can release more energy.  Once this begins to happen, the star has only days until the end.

The star Betelgeuse is a Red Supergiant star.  It is a very red star in the constellation Orion.  We know that it is very close to the end of its life.  It certainly has no more than 1000 years to survive, and maybe far less.  It could explode into a supernova tomorrow -- we have no way of knowing. In fact, perhaps it already has exploded and we just haven't found out yet. Betelgeuse is 560 lightyears away, and so it takes light 560 years to reach us.

While all of this is happening, the outer appearance of the star changes relatively slowly.  Remember than O and B stars are already very luminous, so as the outer layers expand they tend to move horizontally in the H-R diagram.  Their size increases, but their temperature decreases such that their luminosity is virtually the same.  They tend to follow a zig-zag horizontal path in the H-R diagram, as shown in the figure below.

When light nuclei fuse together, the combination actually has less mass than the sum of the parts.  Thus, when four protons are combined into a helium nucleus, the helium nucleus has less mass than the four protons, despite the fact that they both have the same number of particles.  We say that the mass per nucleon is less in helium than for hydrogen.  The difference in mass is converted into energy, according to Einstein's equation E = mc².  That is where the energy comes from in fusion.  In the fission process, too, where heavy elements are split into lighter ones, the heavy nucleus is actually heavier that the sum of the products it splits into, and the difference in energy is released in the reaction.  If we make a plot of mass per nucleon for all the different types of atoms, we find that there is a minimum mass per nucleon, which coincides with the Fe (iron) nucleus. 

This is a plot of binding energy per nuceon, which is opposite to the mass per nucleon. The peak in binding energy at iron (Fe) corresponds to a minimum in the mass per nucleon. Both fission and fusion release energy as the products come closer to iron, but once iron is reached, this is the minimum energy state and no more energy is available to extract from the nucleus. To either split or fuse iron takes energy rather than releasing it.

That means that if the Fe nucleus splits into smaller nuclei, or fuses into larger nuclei, in either case its mass per nucleon increases.  This extra mass has to come from somewhere, and the only way is to use energy to do it.  So iron sucks up energy rather than releasing it!

In the core of a star, once it starts creating iron it is no longer releasing energy and only degeneracy pressure can hold the star up against the crushing force of gravity.  But the iron keeps piling up until degeneracy pressure is overcome, the star can no longer be supported, and something has to happen.

Remember that degeneracy pressure is due to the electrons all being so close together that they have no other energy states to go into.  This electron degeneracy exerts the pressure that keeps the star up, but when it fails the electrons are actually forced into the nucleus, all of the protons combine with the electrons to form neutrons, and the entire core becomes one big neutron nucleus!  Such a neutron core has its own degeneracy, called neutron degeneracy, which may halt the collapse of the core, but by then the core has shrink (in a fraction of a second) from an object the size of the Earth to an object only 10 km across.  To the outer layers of the star, it is as if the bottom fell out and it all goes crashing into the core.  At the same time, the tremendous gravitational potential energy from the collapsing core is released in that fraction of a second -- over 100 times the amount of energy that the Sun would release over its entire 10 billion year lifetime.  The energy drives the outer layers of the star away in a titanic explosion called a supernova. There is so much energy in a supernova explosion that elements higher in atomic number than iron (Fe) can be created. All of the atoms in the universe that are heavier than iron were created in supernova explosions! This is called the nucleosynthesis of heavy elements. e

If the neutron core is small enough, it will survive the explosion and remain as a bare ball of neutrons of order 10 km in size -- an object known as a neutron star.  If the core is too large, however, even neutron degeneracy cannot support it.  In fact, we know of no other force that can withstand the crush of gravity, and we believe that the matter continues to shrink forever, into a mathematical point of mass.  The space (actually the space-time) around such a point is warped to such an extent that even light cannot escape the region around the mass point, and it creates an object known as a black hole.  We will discuss neutron stars and black holes next time.

Let's go back and look at what happens during the supernova explosion.  As we said, the outer layers are blasted away in an explosion.  It used to be thought that the explosion was just due to the shock wave caused by rebound from the neutron core, but recent theoretical ideas indicate that it is the neutrinos that are released in the explosion that power the outward expansion.  The resulting shock wave propels the outer layers of the star outward at up to 10,000 km/s, and the heating causes the star to shine with a dazzling brilliance.  For about a week, a supernova shines as bright as 10 billion Sun's, and can outshine an entire galaxy of stars.  The ejected gases slowly cool and fade. See "What would happen if Betelgeuse went supernova."

We have not seen a supernova explode in our galaxy since 1604, when Kepler wrote about one.  However, one occurred in 1987 in a satellite galaxy to our own -- one of the Magellenic Clouds.  Here is the story of Supernova 1987A.  Long after a supernova has occurred, the blasted layers of the star appear as a supernova remnant.  Here is a huge list of photos of such remnants. The Crab Nebula is the brightest and nearest of such remnants.

What we have just described is called a Type II supernova. There is also another kind called a Type I supernova. Before we can understand this new type of supernova, we have to talk about what happens when two stars grow up and grow old next to each other--close binary stars.

The description we gave of the lives of stars indicates that higher mass stars live a short time, burn through their hydrogen fuel very quickly, and then end their lives in a supernova explosion.  Meanwhile, lower mass stars live much longer, with a lifetime that depends inversely on mass -- the smaller the mass the longer the lifetime.  Such stars end their lives in a planetary nebula phase and then as a slowly cooling white dwarf.

If we look at binary stars that are really close together, however, we find some puzzling things that do not agree with the foregoing arguments.  For example, Algol (the Ghoul star that represents the head of Medusa), is a close binary star (recall that it is an eclipsing binary star, with one star passing in front of the other every 2.6 days).  When we determine the spectral types of these two stars, and their masses, we find that one is a 3.7 solar mass main sequence star, while the other is a 0.8 solar mass red subgiant star.  What is wrong with this?

A red subgiant has aged off the main sequence, yet these two stars must have been formed together, and hence be the same age.  How can a 0.8 solar mass star be off the main sequence already when a 3.7 solar mass star is still on the main sequence?  The answer is that the lower mass star must once have been higher mass, and the higher mass star must have been lower mass -- but the "aged" star transferred a huge amount of its mass to the other star!  Here is a picture of the interaction, as it progressed over a few million years or so.

The star on the left is initially the more massive star.  It ages off the main sequence first, and becomes a red giant star.  As it expands, it starts losing mass to the smaller companion.  The red giant grows and grows, and more and more of its atmosphere is channelled to the other star, until it is as we see it today.  The red giant is now only 0.8 solar mass, while the companion went from a red dwarf main sequence star to an A type main sequence star, more massive than the Sun.

You can imagine what will happen when the right-hand star, now very massive, accelerates its life cycle and becomes a red giant.  Mass will transfer back!