Chapter 15--Our Sun - Geological Sciences

in the creation of two gamma-ray photons through matter–
antimatter annihilation.
Step 2. A fair number of deuterium nuclei are always present
along with the protons and other nuclei in the solar
core, since step 1 occurs so frequently in the Sun (about
10 38 times per second). Step 2 occurs when one of these
deuterium nuclei collides and fuses with a proton. The
result is a nucleus of helium-3, a rare form of helium with
two protons and one neutron. This reaction also produces
a gamma-ray photon.
Step 3. The third and final step of the proton–proton chain
requires the addition of another neutron to the helium-3,
thereby making normal helium-4. This final step can proceed
in several different ways, but the most common route
involves a collision of two helium-3 nuclei. Each of these
helium-3 nuclei resulted from a prior, separate occurrence
of step 2 somewhere in the solar core. The final result is a
normal helium-4 nucleus and two protons.
Total reaction. Somewhere in the solar core, steps 1 and 2
must each occur twice to make step 3 possible. Six protons
go into each complete cycle of the proton–proton chain, but
two come back out. Thus, the overall proton–proton chain
converts four protons (hydrogen nuclei) into a helium-4
nucleus, two positrons, two neutrinos, and two gamma rays.
Each resulting helium-4 nucleus has a mass that is
slightly less (by about 0.7%) than the combined mass of
the four protons that created it. Overall, fusion in the Sun
converts about 600 million tons of hydrogen into 596 million
tons of helium every second. The “missing” 4 million
tons of matter becomes energy in accord with Einstein’s
formula E mc 2 .About 98% of the energy emerges as
kinetic energy of the resulting helium nuclei and radiative
energy of the gamma rays. As we will see, this energy
slowly percolates to the solar surface, eventually emerging
as the sunlight that bathes Earth. About 2% of the energy
is carried off by the neutrinos. Neutrinos rarely interact
with matter (because they respond only to the weak force
[Section S4.2]), so most of the neutrinos created by the
proton–proton chain pass straight from the solar core
through the solar surface and out into space.
The Solar Thermostat
The rate of nuclear fusion in the solar core, which determines
the energy output of the Sun, is very sensitive to
temperature. A slight increase in temperature would mean
a much higher fusion rate, and a slight decrease in temperature
would mean a much lower fusion rate. If the
Sun’s rate of fusion varied erratically, the effects on Earth
might be devastating. Fortunately, the Sun’s central temperature
is steady thanks to gravitational equilibrium—the
balance between the pull of gravity and the push of internal
pressure.
Outside the solar core, the energy produced by fusion
travels toward the Sun’s surface at a slow but steady rate. In
this steady state, the amount of energy leaving the top of
each gas layer within the Sun precisely balances the energy
entering from the bottom (Figure 15.8). Suppose the core
temperature of the Sun rose very slightly. The rate of nuclear
fusion would soar, generating lots of extra energy. Because
energy moves so slowly through the Sun, this extra
energy would be bottled up in the core, causing an increase
in the core pressure. The push of this pressure would temporarily
exceed the pull of gravity, causing the core to expand
and cool. With cooling, the fusion rate would drop
back down. The expansion and cooling would continue until
gravitational equilibrium was restored, at which point the
fusion rate would return to its original value.
An opposite process would restore the normal fusion
rate if the core temperature dropped. A decrease in core
temperature would lead to decreased nuclear burning,
a drop in the central pressure, and contraction of the core.
As the core shrank, its temperature would rise until the
burning rate returned to normal.
The response of the core pressure to changes in the
nuclear fusion rate is essentially a thermostat that keeps
the Sun’s central temperature steady. Any change in
the core temperature is automatically corrected by the
change in the fusion rate and the accompanying change
in pressure.
While the processes involved in gravitational equilibrium
prevent erratic changes in the fusion rate, they also
ensure that the fusion rate gradually rises over billions of
years. Because each fusion reaction converts four hydrogen
nuclei into one helium nucleus, the total number of independent
particles in the solar core is gradually falling. This
gradual reduction in the number of particles causes the
solar core to shrink.
The slow shrinking of the solar core means that it must
generate energy more rapidly to counteract the stronger
compression of gravity, so the solar core gradually gets
hotter as it shrinks. Theoretical models indicate that the
Sun’s core temperature should have increased enough to
raise its fusion rate and the solar luminosity by about 30%
since the Sun was born 4.6 billion years ago.
How did the gradual increase in solar luminosity affect
Earth? Geological evidence shows that Earth’s surface temperature
has remained fairly steady since Earth finished
forming more than 4 billion years ago, despite this 30%
increase in the Sun’s energy output, because Earth has its
own thermostat. This “Earth thermostat” is the carbon
dioxide cycle. By maintaining a fairly steady level of atmospheric
carbon dioxide, the carbon dioxide cycle regulates
the greenhouse effect that maintains Earth’s surface temperature
[Section 14.4].
“Observing” the Solar Interior
We cannot see inside the Sun, so you may be wondering
how we can know so much about what goes on underneath
its surface. Astronomers can study the Sun’s interior in
three different ways: through mathematical models of the
chapter 15 • Our Star 503