29:50 Modern Astronomy
Fall 2002
Lecture 19 ...October 21, 2002
Stellar Evolution of Massive Stars

Last time I described the post-Main sequence evolution of a star like the Sun. The end product will be a White Dwarf star. The white dwarf will have a large fraction of the mass of the original star; 0.60 to 1.4 solar masses, depending on the initial mass of the star. The radius of this core should be of order 7000 kilometers, in comparison with 696,000 for the Sun, and 6378 for the Earth. This core would consist of an entire solar mass crammed into a sphere roughly the size of the Earth. The density of such an object would kg/m compared with 1000 kg/m for water. The density of a white dwarf is the equivalent of 3 metric tons per cubic centimeter. Sirius B....a white dwarf

The story of modern astrophysics for the future history of the Sun is therefore as follows. In about 5 billion years, the hydrogen fuel in the core of the Sun will be exhausted. This will indicate the end of the Main Sequence lifetime of the Sun. It will evolve off the Main Sequence, meaning its outer layers will expand, its surface temperature will drop, and it will be much more luminous. It will become a red giant. When you look up in the sky at night and see bright red stars, you see the future of the Sun. During this period of time, the deep interior of the Sun will be accumulating an increasing fraction of the mass of the star. The material in the core will become increasing chemically differentiated as it goes through different nuclear reactions.

In the late stages of red supergiant evolution, the star will throw off its outer layers into space. Some of the matter which presently forms the Sun will be put back into the space between the star. This will reveal the bright, dense inner core of the star. Eventually, the outer layers disappear and the core is left by itself. The term for this core is a white dwarf star.

As mentioned last time, there is good observational evidence for all of the phases of post main sequence evolution of solar-type stars, and in particular, we see examples of white dwarf stars.

High Mass Stellar Evolution

In stellar evolution, ``mass determines fate''. What I have described is the course of stellar evolution for so-called low mass stars, which are those with masses roughly equal to that of the Sun to a few times that of the Sun. The mass of the ``heavyweights'' is quite a bit different.

The history of a massive star, say 10, 15, or 20 times the mass of the Sun is the same as that of a solar type star through the formation of the C,O core.
Viewgraph of structure of a star.
The difference is that every piece of the star is much more massive, including the core, which instead of 0.8 - 1.0 solar masses, might have 10 solar masses. The force of gravity is much stronger, and the core continues to contract.
Illustration of interior of evolved star.
The only way it can balance this gravitational contraction is again by reaching hydrostatic equilibrium. This means it must find some new nuclear reaction to supply heat. Essentially, the core of such a star has to explore nuclear physics book for nuclear reactions it can use to balance the extremely strong gravitational force.

The core contracts and its temperature and density continue to go up. At a temperature of K, a nuclear reaction involving fusion of carbon nuclei can progress.

The net effect of these nuclear reaction is that carbon is transformed into Neon and Magnesium. The interior of a massive star is a giant synthesizer of elements.

The star quickly exhausts this cycle and begins contracting again. To keeps itself from gravitationally collapsing to a point, it has to find a new nuclear reaction cycle. Nuclear astrophysicists can figure out what the sequence is, such as the density of the core, the nuclear reaction that the star ``finds'' to keep itself supported, and how long this new phase will last.

Table with nuclear reactions, timescales, temperatures, and densities.
This table shows the succession of stages for a 25 solar mass star. The first column gives the nuclear reaction occurring in the core. the second gives the temperature in the core, which is necessary for that reaction to proceed. The third column gives the density of the core, and the final column gives the length of time the star can maintain itself in hydrostatic equilibrium with energy obtained from that nuclear reaction. In the case of this star, hydrogen fusion or the Main Sequence lifetime is 7 million years rather than the 10 billion of the Sun.

In the set of nuclear reactions given above, I went as far as describing nuclear reactions in which carbon nuclei fused to form Neon and Magnesium. This table shows that this phase occurs at a temperature of 200 million degrees Kelvin, a density of 200,000 grams /cm (200 thousand times that of water), and that the star can maintain itself in this condition for 600 years; pretty short on a cosmic timescale.

Following this phase, there are a number of others, ending up with a state in which silicon nuclei fuse to form iron. The table shows that this occurs at a temperature of K, 200 times the temperature in the center of the Sun, and at a density of grams/cm . This is a density of kg/m or 30 million times the density of water. By comparison, metals like gold and lead have densities about 20 times that of water.

The structure of a star in this condition is also amazing, and really shows the Viennese Torte structure.
Figure 20-7 from book.
The outer parts of the star are mainly hydrogen and helium, as are all stars. Deep in the interior we find the core. This core contains a shell of helium, which is the result of the proton-proton cycle. Inside this shell is a shell in which helium is undergoing fusion reactions to form carbon. Inside that is a shell consisting which is inert carbon and oxygen.

Finally, at the very center is a core which is iron. One might think that one could continue up the periodic table of the elements. However, at this point there is a qualitative change in the nature of the star, and a catastrophe occurs.

The famous Curve of Binding Energy shows that iron is the most tightly bound of all nuclei. The consequence of this is that nuclear reactions which synthesize nuclei with smaller atomic weights than iron from lighter nuclei are exothermic meaning that they give off energy. A star uses this fact to generate energy from its nuclear reactions. For nuclei more massive (having higher atomic weights) than iron, the nuclear reaction are exothermic, meaning it takes energy to produce the heavier nuclei.

In fact, the Curve of Binding Energy is declining for nuclei heavier than iron, meaning that nuclear reaction which convert a heavier nucleus into a lighter one release energy. This was again realized in the 1930's and was the basis of the Uranium and Plutonium fission bombs which the United States developed in the Manhattan Project during World War II.

The consequences of all of this for the evolution of massive stars is as follows. A star which finds itself in the configuration of the star at the left finds itself without support. There is no higher nuclear fusion reaction which can release energy necessary to keep the temperature high. As a result, the internal pressure support is inadequate to support the star against its own gravity, and the core of the star collapses. The time scale for this collapse can be calculated to be 1/4 of a second.

As the core collapses a strange transformation occurs. The density of matter, which started out at grams per cubic centimeter, begins to approach that of matter in the nuclei of atoms, which is g/cm , or kg/m . At these densities all of the nuclei begin to merge together in a big soup, and electrons and protons begin combining to form neutrons, in a process called inverse decay:

Where the indicates a neutrino.

The effect of this collapse is to convert the core of the star, which was iron, into a huge ball of neutrons. This ball of neutrons has a mass of order a solar mass. However, since it was crammed to the densities of nuclear matter, it has a radius of only about 10 kilometers. They are not much bigger than Iowa City!

Neutron Degeneracy. A fluid of neutrons at nuclear densities is extremely incompressible meaning that you can't squish it to higher densities. The physical term for this is neutron degeneracy. The consequences of this for astronomy are that during the core collapse of a star, it forms at its very center, a tiny, infinitely (or almost so) hard floor. Flowing into this hard inner boundary is a huge amount of mass flowing at a very high speed. It has a tremendous amount of kinetic energy, which has to go some where because the inward flow is stopped by the neutron star.

The energy is converted into the energy of a gigantic explosion, which blows off all the matter into space, leaving the neutron ball as the only remnant of the star. One can calculate the amount of energy released in this explosion, and indeed we do so in another introductory astronomy course. The energy released is of order Joules. Again, this number is so large as to be practically unimaginable. To give some correspondence, this is in the ballpark of the total energy radiated by the Sun during its 10 billion year Main Sequence lifetime.

To sum things up, this story predicts that the end result of stellar evolution for massive stars should produce the following:

• A titanic explosion at the end of the star's lifetime, which releases in one pop as much energy as it has radiated over its entire lifetime. This explosion would be as luminous as all the other stars in a large galaxy at maximum brilliance.
• A hurling into space of many solar masses worth of heavy elements which have been synthesized in the interior of the star. Thus massive stars pollute the interstellar medium with Neon, Silicon, Iron, and other elements more massive than Hydrogen and Helium.
• The weirdest prediction is the formation of a Neutron Star where the core of the star once was. This object can be described as an atomic nucleus 10 miles in diameter. These objects are so massive and so compact that the escape speed from their surfaces is 25 % that of light.
• At the time the core collapses, there should be a tremendous pulse of neutrinos formed as the core converts from ordinary matter to a neutron fluid.

Observational Verification of Massive Star Evolution

Supernovae At rare intervals through history, there have been recorded examples of the sudden appearance of an extremely bright star. These stars are recorded to gleam for a few weeks, then slow fade in brightness until they disappear from sight. Perhaps the most famous example is the ``guest star'' of 1054 AD, which was extensively described in Chinese chronicles. It occurred in the constellation of Taurus, and for several weeks was bright enough to be seen in broad daylight.

In the 1500's the famous astronomers Tycho and Kepler each saw such a bright but temporary ``new star''.

In the modern era we have seen many examples of these objects occurring in other galaxies. From these studies, we know that such objects occur in a galaxy like the Milky Way about every 50 to 100 years. An illustration is shown in Figure 20-6 of your textbook, on p446.

In 1987, we were fortunate enough to see one of these ``up close''. This was a supernova called 1987A. A striking illustration of the phenomenon is shown in figure 20-10 of your textbook, on p459.
You can see the dramatic increase in the brightness of this star.

One of the important aspects of SN1987A is that it was the first time we were able to see and measure the characteristics of the progenitor star of the supernova. It was indeed a highly luminous, highly evolved star. In 1993, a second supernova occurred in the nearly galaxy M81 for which the progenitor could be identified. It was a red supergiant, which again is consistent with the ideas presented here.

The phenomena of supernova fill the bill for the gigantic explosions demanded by the description of massive star evolution I have been describing. The energy released is indeed in the ballpark of Joules. In the two cases for which we have been able to see the progenitors, we indeed find that they are highly evolved, post Main Sequence stars.

Neutron Stars Certainly the strangest prediction of the above theory was of neutron stars. Where would we look for such objects, and what would their observational signature be? I can recall considerable discussion in the 1960's about these objects, and speculation about whether they existed or were just exotic predictions of theoretical physics. The evidence that they do exist came in 1968, with the announcement of the discovery of pulsars.

The first pulsars were discovered at Cambridge University in England by a graduate student, Jocelyn Bell, and her advisor Anthony Hewish. The observational signature was a very regular series of pulses or ``clicks'' of radio emission from certain directions in the sky.
Drawing of pulsar pulses from 0329+54.
The transparency says this pulsar has a period of 0.714 seconds. As some of you know, there is a brand of watch called Pulsar. It is a good astronomical object to name a watch after. The sequence of these pulses are extremely regular. For example, if you look up the period of this pulsar in a reference book, you will find that its measured value is P = 0.71451866398 seconds. Every one of these numbers is significant. The fact that you can list so many significant figures is an indication that it is a very good clock. It has a slowdown rate which has been measured and is seconds per second. This means that after one year its period will have increased by 0.000000066 seconds.

The periods of pulsars show a wide range, from about 1.6 milliseconds on the short end, to about 3 seconds on the long end. For about a year after their discovery, there was an extensive debate as to what they might be. The main problem was to come up with an object which could both have such a precise, clock like frequency and also have such a short pulse period, typically under a second.

In the end, the theory which emerged was the Rotating Neutron Star model. Its acceptance heralded the observational discovery of neutron stars. The rotating neutron star model is illustrated in this transparency.
Diagram of rotating neutron star model of pulsar.
Pulsar lecture demonstration.
In the rotating neutron star model, the period of the pulses is identified with period for the neutron star to turn on its axis. Evidently there is a beam of radio emission directed along the magnetic axis of the pulsar. When this beam passes across the radio telescope, the observer sees a pulse of emission.

The rotating neutron star model has been extensively corroborated through the years by other independent tests; I would categorize the status of these objects today as being as secure as the existence of moons and other stars.

I can remember following with interest the discussions in the mid 1960's about whether neutron stars existed at all. At that time, they seemed unimaginably weird objects (as indeed they are), and it seemed almost beyond belief that they would exist anywhere in the universe.

In the late 1960's pulsars were discovered, and the case eventually made that these must be neutron stars.

Last Fall, the 1000th radio pulsar was discovered, with more being discovered all the time. To give some visual effect, the map shown here is from a journal article of about 15 years ago, when there were 330 of them known. This map is a projection of the sky. Each dot indicates a pulsar. Each of these dots is ball about the size of Iowa City, having the mass of the Sun, and which was formed in the violent collapse of the core of a massive star.
map of pulsar positions on the sky. In addition to the 1000 radio pulsars, there are other classes of objects which have neutron stars such as low mass x-ray binaries, x-ray pulsars, and an object called SS433. There are probably about 100 objects known in these other categories. Thus is a period of thirty years, neutron stars have gone from being weird figments of the imaginations of theoretical physicists, to common members of the astronomical universe.

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