Helioseismology

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Another probe of the Sun's interior uses the pulsating motions of the Sun. The pulsations are too small to be seen just by looking at the Sun. But the pulsations can be seen if the doppler shifts are measured across the face of the Sun. Some parts of the Sun expand towards the Earth and adjacent regions contract away from the Earth. These regions are several thousands of kilometers across and the pulsation periods are just a few minutes long. Different types of oscillating waves combine to produce the complicated patterns of pulsation seen.

One type of pulsation is shown here. The blue regions are approaching and the red regions are receding from you. The pulsations are thought to extend far into the Sun's interior (courtesy of the National Solar Observatory).

If you disentangle the different oscillation modes from each other, you can use these waves to probe the solar interior. How those waves propogate through the Sun and interact with each other depends on the temperature, density, and composition of the material they pass through. By observing the effects of these waves on the photosphere of the Sun, you can determine the temperature, density, and composition of the different layers inside the Sun. Geologists on the Earth use similar techniques to study the interior of our planet from earthquake waves in the research field called seismology. Modifying the name for solar studies, the study of the Sun's interior using the solar oscillations is called helioseismology.

Solar astronomers have set up a global network of stations to continuously monitor the Sun's pulsations. This network is called the Global Oscillations Network Group (GONG). Links to web sites describing GONG and other helioseismology sites are given below. Instruments to detect solar oscillations have also been placed on satellites. Check the links below for more information about them.

Links to Centers Probing the Sun's Interior

1. The GONG homepage at the National Optical Astronomy Observatories is a must see. A concise fact sheet for GONG is available, as well as, information about helioseismology in general.
2. The Solar Oscillations Investigation at Stanford is another major center for helioseismology research.
3. The Stanford group have also constructed an excellent resourse site for K-12 students called The Solar Center. Many educational activities are available, along with excellent images, movies, and audio (yes, you can hear the Sun pulsate!---the doppler observations have been converted into sound).
4. The Marshall Space Flight Center's Solar Physics web site is an excellent starting point for all the research about the Sun. Links to the space missions and the science background about the Sun are given here.

Vocabulary

Review Questions

1. How does nuclear fusion produce energy?
2. Why does nuclear fusion need high temperatures and densities?
3. Why is it so hard to develop nuclear fusion as a dependable power source on Earth?
4. Why will chemical reactions or gravitational contraction not work for powering the Sun?
5. What is the net result of the nuclear fusion chain process? Why does nature use the complicated chain process instead of a one-step fusion procedure?
6. Where are neutrinos produced? What information can they tell you about interior conditions in the Sun?
7. What is the solar neutrino problem? What could be possible solutions to it?
8. How can you use pulsations of the Sun to find out about the structure and composition of its interior?

Interior Structure of Stars

Mathematical Models

1. Temperature---a measure of the random motion energy (the average kinetic energy) of the gas particles. The higher the temperature, the more random kinetic energy is present.

2. Pressure---the amount of force/area. Hot gas expands to create pressure on its surroundings. For example, the gas inside a hot air balloon pushes out on the material of the balloon enclosing the gas.

3. Mass Density---the amount of mass/volume. Gaseous material can be compressed to smaller volumes and higher densities.

Equation of State

Gravity Holds a Star Together

Hydrostatic equilibrium: gravity compression is balanced by pressure outward.

Greater gravity compresses the gas, making it denser and hotter, so the outward pressure increases.

In any given layer of a star, there is a balance between the thermal pressure (outward) and the weight of the material above pressing downward (inward). This balance is called hydrostatic equilibrium. A star is like a balloon. In a balloon the gas inside the balloon pushes outward and the elastic material supplies just enough inward compression to balance the gas pressure. In a star the star's internal gravity supplies the inward compression. Gravity compresses the star into the most compact shape possible: a sphere. Stars are round because gravity attracts everything in an object to the center. Hydrostatic equilibrium also explains why the Earth's atmosphere does not collapse to a very thin layer on the ground and how the tires on your car or bicyle are able to support the weight of your vehicle.

Long before astronomers knew about nuclear fusion, they had a good idea of how the density and temperature of stars increased toward their cores. Deeper layers have more gravity compression from the overlying layers. The greater gravity compression raises the density of the gas. In order to balance the greater gravity compression, the outward pressure of the gas and radiation is increased by raising the temperature. Calculating the change in density and temperature layer by layer toward the center of a star, you find the temperature at the core of a star = 8 to 28 million K and the densities = 10 to 130 times the density of water. As stars age, these numbers increase! You have already seen in the previous section that hydrostatic equilibrium also provides a ``thermostatic control'' on the energy generation inside a star and keeps the star stable.

Other Pieces

1. Continuity of Mass: the total stellar mass = sum of all of the shell layer masses. Mass is distributed smoothly throughout star's interior (there are no gaps or pockets of ``negative'' mass). Also, the law of the conservation of mass says that the total amount of mass does not change with time.
2. Continuity of Energy: the amount of energy flowing out the top of each shell layer in a star = the amount of energy flowing in at bottom of the shell layer. No energy is magically destroyed or created from nothing. A star's luminosity = sum of all of the shell layer energies. Also, the law of the conservation of energy says that the total amount of energy does not change with time. Energy can change from one form to another form of energy, but the total amount is a constant.
3. Energy Transport: Recall from the discussion about how energy flows in planetary atmospheres that energy moves from hot to cold via conduction, radiation, or convection. Nature will first try to use radiation (photons) to move energy from the very hot interior to the very cold space. If radiation cannot transport all of the energy over the distance from the center to the surface of the star, then nature will also use convection. Convection is the bulk motion of gases used to transport energy. Hot gases rise to the upper levels and radiate their extra energy at the upper levels while cooler gases sink to pick up more energy from the hot interior. Conduction transports energy by having each atom transfer its energy to the atom next to it. Conduction is not an efficient process in a gas so it transports a very small amount of energy in stars and is usually ignored.
4. Opacity: It takes a LONG time for photons produced by nuclear reactions in the core to reach the surface. In the opaque interior a photon travels only about 1 centimeter before it runs into an atom or ion and is absorbed. A measure of the gas' ability to absorb the photons is called its opacity. You cannot see into the interior of a star because the gas has a high opacity.

   The photon is later re-emitted but in a random direction. It may be re-emitted in the direction it came from! So the photon travels a very zig-zag sort of path outward. It takes about a million years for a photon to travel from where it was created in the core to the surface where it is finally released into space. Along the way the photon has transferred some its energy to the gas particles, so the photon has changed from very high energy gamma rays to the lower energy visible light photons. Some of the radiation is also in the form of neutrinos. The gas has almost zero opacity with the neutrinos so they pass right on through the star's gas in just a few seconds.

5. The equation of state, hydrostatic equilibrium and the other physical principles are put together for each layer in a star. The equations are solved for each layer starting from the layer there is direct information of, the surface. That result gives the conditions for the next layer's equations. Solving the layer's equations gives the conditions for the layer below it and this process continues on down toward the center layer by layer. In order to get sufficient detail for accurate results, the star's interior is divided into hundreds of layers. To save on time, the equations are solved using a computer.

Mass-Luminosity Relation Explained

Massive stars have greater gravitational compression in their cores because of the larger weight of the overlying layers than that found in low-mass stars. The massive stars need greater thermal and radiation pressure pushing outward to balance the greater gravitational compression. The greater thermal pressure is provided by the higher temperatures in the massive star's core than those found in low-mass stars. Massive stars need higher core temperatures to be stable!

The nuclear reaction rate is very sensitive to temperature so that even a slight increase in temperature makes the nuclear reactions occur at a MUCH higher rate. This means that a star's luminosity increases a lot if the temperature is higher. This also means that a slight increase in the mass of the star produces a large increase in the star's luminosity.

Mass Cutoff Explained

Stars with too little mass do not have enough gravitational compression in their cores to produce the required high temperatures and densities needed for fusion. The lowest mass is about 0.08 solar masses or about 80 Jupiter masses. Stars less massive than this do not undergo fusion and are called brown dwarfs. Selecting the brown dwarf link will take you to a site with further information about brown dwarfs and the first one discovered called Gliese 229B.

The boundary between brown dwarfs and big gas planets is fuzzy, though gas planets are thought to form from solid cores accreting interplanetary nebula material, and therefore, should have relatively more heavy elements than a star/brown dwarf which forms from simple gravitational collapse of a gas cloud. A rough boundary between the two is 20 Jupiter masses. The companion orbiting the star Gliese 229 is at this boundary mass. Selecting the picture of Gliese 229 and its companion will take you to the caption for the picture at the Space Telescope Institute.

Stars with too much mass have so much radiation pressure inside pushing outward on the upper layers, that the star is unstable. It blows off the excess mass. The limit is about 100 solar masses. Stars like Eta Carinae and the ``Pistol star'' are examples of these supermassive stars. The picture of Eta Carinae below shows two dumbbell-shaped lobes of ejected material from the star in an earlier episode of mass ejection. Selecting the image will take you to more information about the image at the Space Telescope Institute.

The picture below from the Hubble Space Telescope shows the violet Pistol Star surrounded by hydrogen gas fluorescing from the copious ultraviolet light coming from the star. Selecting the image will bring up the press release from the Space Telescope Institute.

Vocabulary

Review Questions

1. How can you determine what the interiors of stars are like?
2. What three quantities does an equation of state relate?
3. What is the equation of state for gases? (Almost any gas has this equation of state, even the air in your automobile tires or air-filled ball.)
4. Use the equation of state of a gas to explain in what way the temperature of the gas changes as the pressure exerted on the gas is increased. Explain why the pressure in your automobile tires is slightly less when they are cold than right after a long drive.
5. What is being equilibrated in hydrostatic equilibrium? How does hydrostatic equilibrium explain why the temperature and density increases inward toward the core of a star?
6. How does hydrostatic equilibrium control the fusion rate in the Sun?
7. What would happen to the size of a star if its core steadily produced more energy than it did at some earlier time (e.g., when a main sequence star becomes a red giant)?
8. What would happen to the size of a star if its core steadily produced less energy than it did at some earlier time (e.g., when a star stops fusing nuclei in its core)?
9. Do photons produced in the core zip right out from the Sun or does it take longer? Explain why.
10. Why do brown dwarfs not undergo fusion?
11. What are some basic differences between stars and planets?

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last update: 07 April 1999