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Stellar Nucleosynthesis

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Hydrogen and helium and some lithium, boron, and beryllium were created when the universe was created. All of the rest of the elements of the universe were produced by the stars in nuclear fusion reactions. These reactions created the heavier elements from fusing together lighter elements in the central regions of the stars. When the outer layers of a star are thrown back into space, the processed material can be incorporated into gas clouds that will later form stars and planets. The material that formed our solar system incorporated some of the remains of previous stars. All of the atoms on the Earth except hydrogen and most of the helium are recycled material---they were not created on the Earth. They were created in the stars.

The use of the word ``created'' here is different than what is normally meant by scientists. In chemical reactions, different atoms or combinations of atoms are said to be produced or created when a reaction takes place. For example, in the Earth section of the planets chapter, I said that oxygen was produced in the photosynthesis process of plants. That oxygen then goes into the air and you breathe it in. To be more correct I should have said that the oxygen atoms were moved or broken off from one set of compounds [carbon dioxide (CO2) and water (H2O)] to form a molecule of two oxygen atoms bound together (O2) and a molecule of carbohydrate made of carbon atoms, hydrogen atoms, and oxygen atoms (C6H12O6). Each atom is rearranged or re-used. It was much simpler to say that oxygen was ``created'' as a by-product of the photosynthesis process. I hope you did not mind. In defense I want you to know that practically everyone, except for the astronomer researching stellar evolution, uses this loose meaning of ``creation''.

However, now that you know about stellar nucleosynthesis, I need to be more careful about what is being created from scratch and what is being re-used. Except for the hydrogen and most of the helium atoms, all of the materials around you, in the food you eat and drink, in the air you breathe, in your muscles and bones, in the paper and ink or toner of this book (or computer screen you are reading), everything (!) are made of atoms that were created in the stars. Those atoms are rearranged to produce the vast variety of things around and in you. In the cores of stars or in supernova explosions, new atoms are manufactured from nuclear fusion reactions. You will find out where the hydrogen and most of the helium atoms came from in the cosmology chapter.

The atoms heavier than helium up to the iron atoms were made in the cores of stars. The lowest mass stars can only synthesize helium. Stars around the mass of our Sun can synthesize helium, carbon, and oxygen. Massive stars (M* > 5 solar masses) can synthesize helium, carbon, oxygen, neon, magnesium, silicon, sulfur, argon, calcium, titanium, chromium, and iron. Elements heavier than iron are made in supernova explosions from the combination of the abundant neutrons with heavy nuclei. The synthesized elements are dispersed into the interstellar medium by the supernova explosion. These elements will be later incorporated into giant molecular clouds and eventually become part of future stars and planets (and life forms?)


black hole event horizon giant molecular cloud
helium flash main sequence neutron star
planetary nebula protostar red giant
shell burning stellar nucleosynthesis subgiant
supergiant supernova T-Tauri
white dwarf


  1. Star main sequence lifetime = [star's mass / star's luminosity] × 1010 years.
  2. Star main sequence lifetime = 1010 / (star's mass)(p - 1), where p = 3 for stars more massive than 30 solar masses and p = 4 for stars less massive than 10 solar masses.

Review Questions

  1. What fundamental property of stars determines their evolution?
  2. Why do massive stars last for a short time as main sequence stars but low-mass stars last a long time in the main sequence stage?
  3. How can you detect protostars if the surrounding gas and dust blocks visible light?
  4. How do T-Tauri stars get rid of the surrounding gas and dust from which they formed?
  5. What is happening in the core of a main sequence star and why is it so stable?
  6. What happens to a main sequence star that has stopped fusing hydrogen in its core?
  7. Are all red giants or supergiants very massive stars? Why are red giants so big and red? What is going on inside the giants?
  8. What is the evolution sequence for stars around the mass of our Sun? How long is the Sun's main sequence lifetime?
  9. What will happen to a hot, blue star (> 10 solar masses) during its entire lifetime?
  10. What will happen to a cool, red star (< 0.5 solar masses) during its entire lifetime?
  11. In which stage is most of a star's mass lost?
  12. How is a planetary nebula formed? What is formed at the center of the planetary nebula? Which main sequence stars will eventually form planetary nebulae?
  13. What happens in a supernova explosion? Which main sequence stars will eventually go supernova?
  14. How can you distinguish planetary nebulae and supernovae from each other and from ordinary H II regions?
  15. About how often does a supernova occur in a typical galaxy? Why is it better to look for supernovae in other galaxies?
  16. How does the concept of stellar nucleosynthesis explain where all of the elements on the Earth came from?
  17. Why is iron the limit for stellar nucleosynthesis in red giants? Where did heavier elements than iron come from?

Confirmation of Stellar Evolution Models

Even the short-lived massive stars last longer than the entire span of human history, so how can astronomers test the predictions of their stellar evolution models? In science the sole judge of scientific truth is experiments or observation. Regardless of how nice or beautiful a scientific theory may appear, if it does not make accurate testable predictions, it is invalid. When color-magnitude (HR) diagrams for star clusters are constructed, there is a convincing confirmation of our stellar evolution models.

What is nice about clusters is that differences in the stars can be explained in terms of only one variable: mass. Stars in a cluster all form at about the same time, so age differences is not a factor in our analysis. The stars form from the same gas cloud, so their chemical composition is the same and all of them are at about the same distance from us, so any differences in apparent brightness are due to luminosity differences. More luminous main sequence stars are more massive than dimmer main sequence stars.

Comparison of the theories with reality is easy since you need to only consider how mass affects the cluster stars' evolution. The predictions from the stellar evolution models as to what the characteristics of the stars in different clusters should be are compared with reality. Star formation and stellar evolution models are confirmed by observations of real clusters. By observing clusters of different ages, you can piece together how a star will form, live, and die.

young cluster history

old cluster history

Finding the Ages of Clusters

Cluster color-magnitude diagrams change with age. More massive stars evolve quicker than low-mass stars. The hot, luminous main sequence stars will die before the cool, dim main sequence stars. This means that an old cluster will have only the low-mass stars still on the main sequence, but a young cluster will have both high and low-mass stars on the main sequence.

The most massive star still on the main sequence tells us the age of the cluster. That point on the main sequence is called the main sequence turnoff. All stars in a cluster are assumed to have formed at about the same time (observations of current star formation do show that stars form in batches). Stars slightly more massive than the turnoff point have already evolved away from main sequence. The most accurate age for a cluster is found from fitting the entire cluster HR diagram (main sequence, sub-giant, red giant, and horizontal branch) to a stellar evolution model of a specific age and chemical composition.

  1. For the common lower mass stars (< 10 solar masses),
    lifetime = (1010) / (Mass3) years.
    Use solar masses!
  2. For the rare massive stars (> 30 solar masses), use
    lifetime = (1010) / (Mass2) years.


main sequence turnoff

Review Questions

  1. How do cluster H-R diagrams confirm the stellar evolution models?
  2. How can you use a cluster's H-R diagram to find the age of the cluster? What can the main sequence turnoff (MST) tell you?
  3. What assumptions are made in the age-dating method of the main sequence turnoff?
  4. How do you know that a cluster with a MST of 3 solar masses is younger than a cluster with a MST of 2.8 solar masses and older than a cluster with a MST of 3.2 solar masses?

Stellar Remnants

All that is left of the star after the outer layers are ejected to space is the core remnant. The core's gas is super-compressed by gravity to form a strange type of gas made of ``degenerate matter''. It is important to remember that what happens to the core depends on the mass of the core, rather than the original mass of the main sequence star from which it came, because the only thing left for gravity to really compress is the core.

Degenerate matter

When gas become super-compressed, particles bump right up against each other to produce a kind of gas, called a degenerate gas, that behaves more like a solid. Normal gas exerts higher pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on the temperature. The laws of quantum mechanics must be used for gases of ultra-high densities.

The first rule is that only certain energies are permitted in a closely confined space. The particles are arranged in energy levels like rungs of an energy ladder. In ordinary gas, most of the energy levels are unfilled and the particles are free to move about. But in a degenerate gas, all of the lower energy levels are filled. The second rule is that only two particles can share the same energy level in a given volume at one time. For white dwarfs the degenerate particles are the electrons. For neutron stars the degenerate particles are neutrons. The third rule is that how close particles can be spaced depends inversely on their masses. Electrons are spaced further apart in a degenerate electron gas than the neutrons in a degenerate neutron gas because electrons are much less massive than neutrons.

Let's see how these rules affect the core remnant.

  1. Degenerate gases strongly resist compression. The degenerate particles (electrons or neutrons) are locked into place because all of the lower energy shells are filled up. The only way they can move is to absorb enough energy to get to the upper energy shells. This is hard to do! Compressing a degenerate gas requires a change in the motions of the degenerate particle. But that requires A LOT of energy. Degenerate particles have no ``elbow room'' and their jostling against each other strongly resists compression. The degenerate gas is like hardened steel!

    energy levels of degenerate matter

  2. The pressure in a degenerate gas depends only on the speed of the degenerate particles NOT the temperature of the gas. But to change the speed of degenerate particles requires A LOT of energy because they are locked into place against each other. Adding heat only causes the non-degenerate particles to move faster, but the degenerate ones supplying the pressure are unaffected.

  3. Increasing the mass of the stellar core increases the compression of the core. The degenerate particles are forced closer together, but not much closer together because there is no room left. A more massive stellar core remnant will be smaller than a lighter core remnant. This is the opposite behavior of regular materials: usually adding mass to something makes it bigger!

adding mass SHRINKS size

White Dwarfs

White dwarfs form as the outer layers of a low-mass red giant star puff out to make a planetary nebula. Since the lower mass stars make the white dwarfs, this type of remnant is the most common endpoint for stellar evolution. If the remaining mass of the core is less than 1.4 solar masses, the pressure from the degenerate electrons (called electron degeneracy pressure) is enough to prevent further collapse.

what holds degenerate stars up

Because the core has about the mass of the Sun compressed to something the size of the Earth, the density is tremendous: around 106 times denser than water (one sugarcube volume's worth of white dwarf gas has a mass > 1 car)! A higher mass core is compressed to a smaller radius so the densities are even higher. Despite the huge densities and the ``stiff'' electrons, the neutrons and protons have room to move around freely---they are not degenerate.

White dwarfs shine simply from the release of the heat left over from when the star was still producing energy from nuclear reactions. There are no more nuclear reactions occurring so the white dwarf cools off from an initial temperature of about 100,000 K. The white dwarf loses heat quickly at first cooling off to 20,000 K in only about 100 million years, but then the cooling rate slows down: it takes about another 800 million years to cool down to 10,000 K and another 4 to 5 billion years to cool down to the Sun's temperature of 5,800 K.

Their rate of cooling and the distribution of their current temperatures can be used to determine the age of our galaxy or old star clusters that have white dwarfs in them. However, their small size makes them extremely difficult to detect. Because it is above the atmosphere, the Hubble Space Telescope can detect these small dead stars in nearby old star clusters called globular clusters. Analysis of the white dwarfs may provide an independent way of measuring the ages of the globular clusters and provide a verification of their very old ages derived from main sequence fitting. Select the image below to enlarge it.

white dwarfs in a globular cluster
HST image

Novae and Supernovae Type I

An isolated white dwarf has a boring future: it simply cools off, dimming to invisibility. White dwarfs in binary systems where the companion is still a main sequence or red giant star can have more interesting futures. If the white dwarf is close enough to its red giant or main sequence companion, gas expelled by the star can fall onto the white dwarf. The hydrogen-rich gas from the star's outer layers builds up on the white dwarf's surface and gets compressed and hot by the white dwarf's gravity.

Eventually the hydrogen gas gets dense and hot enough for nuclear reactions to start. The reactions occur at an explosive rate. The hydrogen gas is blasted outward to form an expanding shell of hot gas. The hot gas shell produces a lot of light suddenly. From the Earth, it looks like a new star has appeared in our sky. Early astronomers called them novae (``new'' in Latin). They are now known to be caused by old, dead stars. The spectra of a nova shows blue-shifted absorption lines showing that a hot dense gas is expanding towards us at a few thousands of kilometers per second. The continuum is from the hot dense gas and the absorption lines are from the lower-density surface of the expanding cloud. After a few days the gas has expanded and thinned out enough to just produce blue-shifted emission lines.

After the nova burst, gas from the regular star begins to build up again on the white dwarf's surface. A binary system can have repeating nova bursts. If enough mass accumulates on the white dwarf to push it over the 1.4 solar mass limit, the degenerate electrons will not be able to stop gravity from collapsing the dead core. The collapse is sudden and heats the carbon and oxygen nuclei left from the dead star's red giant phase to temperatures great enough for nuclear fusion. The carbon and oxygen quickly fuse to form silicon nuclei. The silicon nuclei fuse to create nickel nuclei. A huge amount of energy is released very quickly with such power that the white dwarf blows itself apart. This explosion is called a Type I supernova to distinguish them from the supernova (called a Type II supernova) that occurs when a massive star's iron core implodes to form a neutron star or black hole. Type I supernovae are several times brighter than Type II supernovae.

Neutron Stars

If the core mass is between 1.4 and 3 solar masses, the compression from the star's gravity will be so great the protons fuse with the electrons to form neutrons. The core becomes a super-dense ball of neutrons. Only the rare, massive stars will form these remnants in a supernova explosion. Neutrons can be packed much closer together than electrons so even though a neutron star is more massive than a white dwarf, it is only about the size of a city.

what holds degenerate stars up

The neutrons are degenerate and their pressure (called neutron degeneracy pressure) prevents further collapse. Neutron stars are about 30 kilometers across, so their densities are much larger than even the incredible densities of white dwarfs: 2 × 1014 times the density of water (one sugarcube volume's worth has a mass = mass of humanity)! Recently, the Hubble Space Telescope was able to image one of these very small objects. It is shown in the figure below (the arrow points to it). Even though it is over 660,000 K, the neutron star is close to the limit of HST's detectors because it is at most 27 kilometers across.

HST sees bare neutron star


In the late 1960's astronomers discovered radio sources that pulsated very regularly with periods of just fractions of a second to a few seconds. The periods are extremely regular---only the ultra-high precision of atomic clocks can show a very slight lengthening in the period. At first, some thought they were picking up signals from extra-terrestrial intelligent civilizations. The discovery of several more pulsars discounted that idea---they are a natural phenomenon called pulsars (short for ``pulsating star'').

Normal variable stars (stars near the end of their life in stages 5 to 7) oscillate brightness by changing their size and temperature. The density of the star determines the pulsation period---denser stars pulsate more quickly than low density variables. However, normal stars and white dwarfs are not dense enough to pulsate at rates of under one second. Neutron stars would pulsate too quickly because of their huge density, so pulsars must pulsate by a different way than normal variable stars. A rapidly rotating object with a bright spot on it could produce the quick flashes if the bright spot was lined up with the Earth. Normal stars and white dwarfs cannot rotate fast enough because they do not have enough gravity to keep themselves together; they would spin themselves apart. Neutron stars are compact enough and strong enough to rotate that fast. The pulsar at the center of the Crab Nebula rotates 30 times every second. In the figure below, it is the left one of the two bright stars at the center of the Hubble Space Telescope image (right frame).

HST view of Crab Nebula pulsar
HST image

Another clue comes from the length of each pulse itself. Each pulse lasts about 1/1000th of a second (the time between pulses is the period mentioned above). An important principle in science is that an object cannot change its brightness faster than it takes light to cross its diameter. Even if the object could magically brighten everywhere simultaneously, it would take light from the far side of the object longer to reach you than the near side. The observed change in brightness would be smeared out over a time interval equal to the time it would take the light from the far side of the object to travel to the near side of the object. If the object did not brighten everywhere simultaneously, then a smaller object could produce a pulse in the same interval. The brightness fluctuation timescale gives the maximum size of an object.

smaller fluctuation timescale means smaller diameter

The 1/1000th of second burst of energy means that the pulsars are at most (300,000 kilometers/second) × (1/1000 second) = 300 kilometers across. This is too small for normal stars or white dwarfs, but fine for neutron stars. When neutron stars form they will be spinning rapidly and have very STRONG magnetic fields (109 to 1012 times the Sun's). The magnetic field is the relic magnetic field from the star's previous life stages. The magnetic field is frozen into the star, so when the core collapses, the magnetic field is compressed too. The magnetic field becomes very concentrated and much stronger than before.

must spin fast to keep (size*spin speed) the same

Why would neutron stars be fast rotators? Conservation of angular momentum! Just as a spinning ice skater can spin very fast by pulling in her arms and legs tight about the center of her body, a star will spin faster when it brings its material closer to its center. The angular momentum of an object = its mass × its equatorial spin speed × its radius. The mass remains constant. In order to keep the angular momentum constant the spin speed must increase if the radius decreases. This will keep the product of spin speed × radius the same value. A slowly rotating red giant star will have the same angular momentum when it becomes a tiny, fast rotating neutron star. See the Angular Momentum appendix for other examples.

spinning ice skater increases spin speed

Lighthouse Model

The spinning neutron star produces beams of radiation that sweep across your line of sight like a lighthouse beam does for ships at sea. In the lighthouse model the neutron star's strong magnetic field creates a strong electric field. The electric field makes charged particles (mostly electrons) flow out of the magnetic poles. As the charged particles spiral around the magnetic field lines, they produce electromagnetic radiation (recall from the electromagnetic radiation chapter that any moving charge will create electromagnetic radiation). The energy is called non-thermal radiation because it is not produced by a hot, dense object, but by accelerated charges. The shape of the continuous spectrum is different from a normal thermal spectrum and does not depend on the temperature. A type of particle accelerator in physics laboratories here on Earth called a ``synchroton'' produces this kind of radiation too, so it is sometimes called ``synchrotron radiation''.

The neutron star's magnetic field lines converge at the magnetic poles, so the charges get focussed and a narrow cone of non-thermal radiation is beamed outward. If the beam sweeps past Earth, you see a flash of light. However, given the wide range of angles the magnetic poles could be aligned in space, it is more likely that the beam will miss the Earth. There are probably many more pulsars out there that cannot be detected because their beams do not happen to cross our line of sight.

why pulsars pulsate

The energy of the non-thermal radiation beam comes from the rotational energy of the pulsar. Since the light energy escapes, the production of the energy beam robs energy from the pulsar so the pulsar's rotation slows down (angular momentum does slowly decrease). Another equivalent way to view the process is from Newton's 3rd law of motion. The magnetic field exerts a force on the charged particles, speeding them up. The charged particles exert a reaction force on the magnetic field slowing it and the pulsar down. Eventually, the pulsar dies away when the neutron star is rotating too slowly (periods over several seconds long) to produce the beams of radiation.

Every now and then, a ``glitch'' is seen in the pulse rate from a pulsar. The pulsar suddenly increases its spin rate. What causes this is the neutron star suddenly shrinks by about 1 millimeter. The spin rate suddenly increases to conserve angular momentum.

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last updated: 01 July 2000

Is this page a copy of Strobel's Astronomy Notes?

Author of original content: Nick Strobel

This page was copied from Nick Strobel's Astronomy Notes. Go to his site at for the updated and corrected version.