The Sun As a Star

Last: 7. The Face of the Sun Next: 9. How Far the Stars?

The Sun is not only the largest object in our solar system -- it is also the nearest example of a star. It produces energy by converting hydrogen to helium, thereby maintaining a nearly-constant internal temperature. Particles emitted by the Sun and detected on Earth confirm the details of this picture.

Topics

Reading

  12.2 Where Stars Get Their Energy   p. 282
    Figure it Out 12.1: Energy Generation in the Sun   p. 283
  12.3 Atoms and Nuclei   p. 283
  12.3a Subatomic Particles   p. 283-284
  12.3b Isotopes   p. 284
  12.3c Radioactivity and Neutrinos   p. 284-285
  12.4 Stars Shining Brightly   p. 285-286
  12.5 Why Stars Shine   p. 286-287
  12.7 The Solar Neutrino Experiment   p. 288
  12.7a Initial Measurements   p. 288-289
  12.7b The Sudbury Neutrino Observatory   p. 289-290

Inside the Sun

The Sun's interior is made up of the same mix of hydrogen and helium as its surface. Below the surface layers, three main regions can be defined. These are the core, where energy is produced, a radiative zone, where this energy travels as radiation, and a convective zone, where energy travels by convection.   Structure of the sun

Composition of the Sun

Spectroscopy enables us to determine the Sun's composition (see Table 10.1):

Number
of Atoms		 Chemical
Symbol		 Atomic
Number		 Atomic
Weight
1,000,000 H 1 1
85,000 He 2 4
850 O 8 16
400 C 6 12
120 Ne 10 20
100 N 7 14
47 Fe 26 56

The Convective Zone

The convective zone extends from 70% of the Sun's radius outward to the `surface' or photosphere. While temperatures in this zone can be very high (millions of degrees), atoms are still able to keep some of their electrons. As a result, the gas is opaque to photons (particles of light energy), and energy is transported outward by the familiar process of convection. This convective motion ultimately accounts for most manifestations of solar activity, including sunspots and the Sun's magnetic field.   Structure of the sun

The Radiative Zone

The radiative zone extends from 20% to 70% of the Sun's radius. In this zone, temperatures are high enough to detach electrons from atomic nuclei, and the gas is said to be ionized. As a result, photons are able to diffuse from the core out toward the surface. This is a slow process -- it takes hundreds of thousands of years for energy to make its way across the radiative zone. Nonetheless, this process is efficient enough that convection is not needed to transport the energy.   Structure of the sun

Our basic picture of the Sun's interior was developed by applying the laws of pressure balance and energy transport to a sphere of hydrogen and helium of known size, mass, and energy output. But recently, a powerful test has become possible...

Helioseismology

To study the Sun's structure, we can use the basically the same method we used earlier for the Earth: monitor vibrations inside the Sun and use the results to check our theories.

The Sun is like a big echo chamber, and sound waves created by turbulence reverberate through its interior. This diagram shows one possible pattern of vibration in the Sun. Notice that the wavelength increases going deeper into the Sun; this implies that the sound speed is increasing.

   Vibration mode inside the sun
Helioseismology [Stanford]

Doppler Shift

To detect solar vibrations, we use the Doppler shift of a spectral line of known wavelength.

This diagram shows the Doppler shift for a source of light waves moving upward. The wavelength is shorter above the source, and lower below. The faster the source moves, the greater the difference in wavelength:

λ - λ0 = v
c  		λ0
where c = 3×1010 m ⁄ sec is the speed of light, and v is the speed of the source. 		  Illustration of the Doppler effect
Doppler effect [Wikipedia]

Question 8.1


Which of the following best describes the way this source of waves is moving?

  1. The source is not moving.
  2. The source is moving up.
  3. The source is moving down.
  4. The source is moving left.
  5. The source is moving right.
   Illustration of the Doppler effect
Doppler effect [Wikipedia]

Doppler Shift

To detect solar vibrations, we use the Doppler shift of a spectral line of known wavelength.

This diagram shows the Doppler shift for a source of light waves moving upward. The wavelength is shorter above the source, and lower below. The faster the source moves, the greater the difference in wavelength:

λ - λ0 = v
c  		λ0
where c = 3×1010 m ⁄ sec is the speed of light, and v is the speed of the source. 		  Illustration of the Doppler effect
Doppler effect [Wikipedia]

Solar vibrations cause the surface layers of the Sun to move up and down with speeds of about 500 m ⁄ sec and periods of about 5 min. Sensitive instruments can detect the shift in wavelength due to this motion and map it across the face of the Sun.

Solar Velocity Maps

Velocity map of the sun
MDI Image Gallery [SOHO (ESA & NASA)]

Solar Flare and Waves

In some cases, `sunquakes' can be observed directly by the Doppler method. This image shows a solar flare which has produced expanding waves like ripples in a pond.   A flare and the wave it produces
MDI Image Gallery [SOHO (ESA & NASA)]

Helioseismology Results

One key result of helioseismology is shown in this plot, which compares the predicted and observed speed of sound at different depths in the Sun. Perfect agreement would be represented by a horizontal line. The variations from perfect agreement are tiny -- less than 0.4% everywhere within the Sun!   Speed of sound: theory - observation
Solar Sound Speed Variations [Stanford]

The Sun's Core

Within the Sun's core, the enormous weight of the overlying material compresses the gas to an almost unimaginable degree. The density of the gas is roughly

ρ = 150 gm ⁄ cm3 ,

or about 150 times the density of water. The temperature is about

T = 1.5×107 K .

   Structure of the sun

Under such extreme conditions, the hydrogen in the core of the Sun is slowly transmuted into helium. One by-product is 4.6 billion years of sunshine, with much more to come.

A Pint of the Sun

Descriptions of nuclear `burning' in stars sometimes give the impression that the central furnace of a star is a place of violent activity. In fact, the inside of a star is rather peaceful, and hydrogen burning goes on very slowly.

To appreciate this, imagine we had a magic transporter which could beam one pint of gas from the center of the Sun right into this room. One pint of water weighs one pound, but the center of the Sun has a density about 150 times the density of water, so a pint of sun-stuff weighs almost as much as I do.

Now the first thing that would happen is that this building would vanish in a huge explosion. When it was down these in the center of the Sun, the gas was compressed by the vast weight of all the thick layers of dense material above it, so it was under enormous pressure. When it's suddenly transported to Earth, the confining pressure is removed, and the gas expands -- very rapidly. The explosion would have the force of a small nuclear bomb.

So if we want to get this experiment approved by the University administration, we need to make a container which can hold our pint of sun-stuff under pressure without bursting apart. That's not easy to do, but we've already assumed we have a transporter right out of Star Trek, so a little more magic won't be noticed. But our troubles are not over, because this gas from the center of the sun is incredibly hot, and the heat would escape in the form of X-rays, cooking everyone in the vicinity.

  

OK, let's assume we can make the walls of our container perfectly reflective, so that all the escaping heat energy is reflected right back in. I said we were using magic, didn't I? So we have a pint of sun-stuff sitting right there in front of us, safe as can be. Now let's allow a little energy to escape -- just exactly the amount of energy being generated by nuclear reactions, so the gas stays at a constant temperature. We can use the escaping energy to run a generator and produce electricity. Thermonuclear power!

But before we call a press conference or make any big deals with HECO, we better figure out how much energy those bottled nuclear reactions are generating. And the answer is...

About a thousand times less energy than I'm generating by breathing. That's all! Per unit mass, the Sun produces much less energy than a living human body. In total, the Sun generates a lot of energy, but that's only because it's so massive. If I was as massive as Jupiter -- perish the thought -- I'd produce more energy than the Sun, just from my body heat.

Of course, the Sun produces energy by nuclear reactions, while I produce energy by chemical reactions. That's how the Sun can go on shining for ten billion years, whereas I get hungry every few hours.

The enormous lifetime of the Sun gives us another perspective on the same basic point, which is that nuclear reactions in stars are, for the most part, very slow and gentle. It takes about ten billion years for all the hydrogen in the center of the Sun to be burned to helium. That means that per year, a hydrogen nucleus has about one chance in ten billion of being involved in a nuclear reaction. The center of the Sun is an incredibly safe place for hydrogen nuclei! A hydrogen nucleus in the Sun runs much less risk of undergoing a nuclear reaction than I do of being hit by lightning.

Energy From Matter

From a physicist's point of view, matter is frozen energy, and under the right conditions each can be converted to the other. The conversion of mass m to energy E is expressed by Einstein's famous equation:

E = m c 2 .

In most people's minds, this equation is associated with nuclear energy, but in fact it applies to any form of energy release.

  Form of Energy  Example Efficiency  
  Chemical Energy  H2 + O → H2O ∼10-8  
  Nuclear Energy  4p → He4 0.007  
  Gravitational Energy  mass → black hole 0.1 - 0.3  

Isotopes of Hydrogen and Helium

H and He isotopes

The chemical properties of an element are determined by the number of electrons orbiting each nucleus -- and since each electron is balanced by a proton within the nucleus, it's also true that the chemical properties are determined by the number of protons in each nucleus. For example, the nucleus of an iron atom has exactly 26 protons.

However, most elements exist in several forms which are distinguished by the number of neutrons also present in the nucleus. These different forms are called isotopes.

Hydrogen and helium have several different isotopes. Hydrogen (1 proton) can have zero, one, or two neutrons. Helium (2 protons) can have one or two neutrons.

The Proton-Proton Chain

In the Sun's core, nuclei of hydrogen atoms (protons) are converted to nuclei of helium atoms:
  1. Two protons (p) fuse, forming one deuteron (d)

    2. This step is very slow, because one p must change into a neutron (n). A neutrino (ν) and a positron are produced.

  2. One p and one d fuse, forming He3, a light helium nucleus

    3.  

  3. Two He3 fuse, producing one He4, two p, and energy.
   Nuclear fusion in the sun
Proton-proton chain reaction [Wikipedia]

Cosmic Gall

From Telephone Poles and Other Poems, by John Updike

Neutrinos: they are very small
They have no charge; they have no mass;
they do not interact at all.
The Earth is just a silly ball
to them, through which they simply pass
like dustmaids down a drafty hall
or photons through a sheet of glass.
They snub the most exquisite gas,
ignore the most substantial wall,
cold shoulder steel and sounding brass,
   insult the stallion in his stall,
and, scorning barriers of class,
infiltrate you and me! Like tall
and painless guillotines they fall
down through our heads into the grass.
At night, they enter at Nepal
and pierce the lover and his lass
from underneath the bed. You call
it wonderful; I call it crass.
Last: 7. The Face of the Sun Next: 9. How Far the Stars?
Joshua E. Barnes (barnes@ifa.hawaii.edu)
Last modified: October 8, 2006
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