Astronomy 124
The Sun: An Introduction to the Stars
In this course, Astronomy 124, we will be learning about the contents
of the universe, from the relatively small scales of a single star
system up to the largest distances known, namely the entire visible
universe. Along the way we will encounter various types of galaxies,
clusters of galaxies, clusters of stars, interstellar gas and dust,
neutron stars and black holes, and, of course, individual stars. The
stars, in fact, are a very basic constituent of the universe so it is
important to get a good grasp on the properties of them. The most
familiar of all the stars is our Sun. Many of the properties of the
Sun will be common to all stars, so we will begin with it.
What are the most obvious properties of the Sun? It's hot and bright.
A slightly more subtle point was recognized by ancient astronomers who
determined that the Sun moves through the sky on a daily and annual
cycles, and that these cycles account for the length of the day and the
seasons of the year. Many ancient structures and monuments (for
example, Stonehenge) are believed to be designed to keep track of these
sky motions. With the coming of the Renaissance and the work of
Copernicus, Galileo, and Kepler it was realized that the observed
motions of the Sun were not a property of the Sun itself, but of the
rotation of the Earth and its orbital motion around the Sun. So what
are we left with? It's hot and gives off light. Let's try to learn
something more.
What is there to know about the Sun? How about its size, mass,
composition, internal structure, temperature, source of its heat and
light, age, and life history? Pause for a moment and reflect upon the
general issue of how one would set about to learn these things. You
can't travel to the Sun. You can't get pieces of it to examine. All
you can do is observe it, and perform experiments on Earth to help you
learn about the laws of nature. With a little thought you might be
able to relate the results of your physics experiments back to what
you are observing in the heavens. This is the way it is with
astronomy.
We begin with a rather straightforward property of the Sun, namely its
size and the distance to it. Note, however, that determining
even something as simple as the size of the Sun is not so
straightforward. You can see the Sun but just how far away is it? If
you know the distance to the Sun then the apparent size of the Sun
directly gives you its diameter. Alternately if you knew how big the
Sun was you would know how far away it was. But you know neither. In
astronomy it is customary to express the apparent size of
something in terms of the angle that the Sun's image takes up on the
sky. (Apparent size is just how big something looks; it is an observed
quantity, not an intrinsic property. The task of the astronomer is to
move from what is observed, that is how things appear to us, to the
general property, how things really are.)
What are the units of angle? Recall that the total angular measure
around a circle is 360 degrees. The angle from (say) the eastern to
western horizon (through the point directly overhead, the zenith) is
180 degrees. The Sun, as it turns out, has an apparent diameter of
about 32 arc minutes (a minute is equal to 1/60th of a degree; a second
of an arc is equal to 1/60th of a minute). Another unit of angle is
the radian which is the angle that
gives an arc of a circle equal to the radius. The advantage of using
the radian as the unit of measure is that you can convert directly from
angular size to a relationship between size of the object and the
distance to it: Specifically, the diameter of an object divided by the
distance to it is equal to its apparent size in radians.
FIGURE: Units of angular measure. The radian is a unit of
measure which gives an arc on a circle equal to the radius of the
circle. It is about 57.3 degrees in size.
Now, given that, one can use the rules of trigonometry to determine the
diameter of the Sun if one knows the distance, or one could
determine the distance if one knew the diameter. But how does one
determine a distance? In the case of the Sun it was done in the same
manner that we determine distances here on the Earth: by the method of
triangulation. It is of some historical interest to note that the size
of the solar system was first measured by observing the planet Venus
crossing over the face of the Sun (in 1761 and 1769) from several
locations on the Earth and triangulating to obtain the distance from
the Earth to Venus. (The observing expedition to Tahiti was led by
Captain James Cook.) Anyway, the average distance from the Earth to
the Sun is 150,000,000 kilometers (1.5 × 108). The angular
diameter of the Sun is 32 arc minutes which is equal to about .009
radians of angle which means that the Sun is about 1.4 × 107
kilometers in diameter (about 110 times that of the Earth). Since in
astronomy we most often refer to the
radius of stars and planets,
and we use the units of centimeters (cm), we shall note that the radius
of the Sun is 7 × 1010 cm.
FIGURE: The diameter of the Sun and its distance away from us are
related by the apparent angular size of the Sun. The ratio of the
diameter to the distance is equal to the size of the angle in
radians.
Next consider the Sun's mass.
Historically it was a major advancement to realize that there was such
a property as mass and what it meant to have a certain mass. On Earth
we think of mass as the amount of "stuff" something has, or how much it
"weighs." Obviously we can't take the Sun and put it on a balance as we
might do if we were measuring the mass of some rock. What other
properties does mass have? Newton is the scientist credited with the major
discovery that mass implies a gravitational attraction between
objects with mass, that is, they exert a pulling force on each other.
Newton worked this out quantitatively and he determined the
mathematical relationship
Fgravity = G M m / R2
describes the force of gravity between two objects of mass M and m
and separated by a distance R (the term G is a constant that
relates the units of mass and distance to those of force). Note that
Newton's Law of gravity tells us that the gravitational force between
two objects rapidly becomes weaker as those objects become further
apart. It also tells us that the force of gravity is stronger in
direct proportion to the mass M.
Hence we measure the Sun's mass by its gravity. The Earth is
maintained in its orbit around the Sun by the gravitational attraction
of the Sun. Newton discovered that if there are two bodies with mass
m1 and m2 orbiting each other, then the size of
the orbit (given by a) is related to the period of the orbit
(specified as P) by the following formula:
P2 G (m1+m2)
= 4 pi2 a3
The general relationship that the orbital period squared is
proportional to the orbital radius cubed is originally due to Kepler
and is known as Kepler's Third law. Throughout this semester we will
be concerned with determining the mass of things, from other stars, to
black holes, to whole galaxies and even the whole universe. The only
way we have to measure mass of such objects is through the
gravitational force that they exert on other objects. (Note: this
material is covered in more depth in Astronomy 121, and is discussed in
Chapter 2 of your text.
We introduce it here simply to show
you how the mass of the Sun can be determined, and by extension the
mass of stars in orbiting binary star systems. Indeed, forms of this
law allow us to estimate the masses of entire galaxies. So this is an
important concept although we must leave out the more extensive
discussion of Newton's laws which would permit a more thorough
understanding of the derivation of Kepler's law.)
Using Kepler's law, the period of the Earth's orbit (1 year), the
size of the orbit (the distance to the Sun given above) and a value for
the constant G in the equation permits us to obtain, through simple
algebraic manipulation, the value of m1 + m2, the
combined mass of the Earth and the Sun. This will be very nearly equal
to the mass of the Sun since the mass of the Earth is completely
insignificant. (If you were weighing an elephant by more or less
conventional means then the presence of a few dust specks on his back
would hardly throw the measurement off by a significant amount.) As it
turns out the mass of the Sun is just about 2 × 1033
grams (gm). For comparison, you weigh about 5 × 104
gm.
(The mass of the Earth can be similarly determined by the orbits of
satellites around it, or, more simply from the acceleration due to
gravity at the Earth's surface.
What was not known for a long time was the
value of the constant of proportionality in Newton's law, namely G.
This was determined by Henry Cavendish in the 1790s by measuring the
attractive force between two objects of known mass. As you should
imagine, this required a very sensitive experiment because the force
of gravity is very weak--G is very small. This experiment has
sometimes been referred to as "weighing the Earth" but it might better
be referred to as "weighing the universe" because it was
the final key piece needed to use Kepler's orbital equation to
determine the masses of the Earth, the Sun, indeed the whole
universe.)
Given the mass of the Sun and its size we can compute its density. The density of something is
equal to its mass divided by its volume. Specifically, for a sphere we
have
rho = M / ( 4/3 pi R3)
where the Greek rho is our symbol for density and the R is the
radius of the sphere. If you plug in the numbers for the Sun you get
a density of 1.4 gm/cm3. For comparison, water
has a density of 1 gm cm3, and rock around 3. So the average
density of the Sun is not all that different from you. (You are about
equal to water as evidenced by the fact that the human body is nearly
neutrally buoyant in water; you float but not well enough to keep your
nose out of the water. Does it surprise you that the Sun is about as
dense as water? Did you think it might be denser because it's big,
or less dense because it's floating in space? Beware of casual
thinking and naive expectations in astronomy!)
Now let's return to the properties of the Sun that we first mentioned:
heat and light. Why is the Sun giving off heat and light? The answer
for the ancients was in terms of a familiar phenomenon: the Sun must be
on fire. A more appropriate analogy for today's more sophisticated
student might be the filament of a light bulb (so long as you don't
conclude that the Sun is powered by electricity.) The point is that
you already have experienced the fact that sufficiently hot things give
off visible light. The Sun, like all stars, is just a hot ball of gas
that is giving off blackbody radiation. Let's examine how the Sun is
hot and why.
Visible Parts of the Sun
When we look at the Sun the surface that we see is called the photosphere. We can only see
down into the Sun until the opacity
is large enough to scatter the light. The deeper that one looks the
higher the temperature. This accounts for the phenomenon known as limb
darkening, which refers to the fact that the Sun appears darker out on
its edge. This is because out at the edge you have to look through a
thicker layer of solar atmosphere (because you are looking slantwise
through it) when compared with the center of the Sun. You see mainly
the higher layers of the photosphere where the temperature is lower,
at about 4000K. At the center you are looking deep into the
photosphere and the temperature is higher and consequently the Sun
appears much brighter. (The same sort of thing happens when you look at
the stars in the sky; stars overhead are less obscured than stars on
the horizon because the stars on the horizon have had to pass through a
greater column of the Earth's atmosphere and so are subjected to more
scattering of their light.)
The surface of the Sun has a mottled appearance called
"granulation." This represents the upper end of the convection
cells that are in the outer layers of the Sun. Convection
is a process by which heat is transported from hot to cool regions
through the physical motion of the gas. Here the convection cells are
places where hot gas boils up from deeper within the Sun.
The center of a
granual, or convection cell, is where the rising hot gas is. Since
the gas has higher temperature it is brighter than the region
surrounding the cell where cool gas is sinking.
Another sort of mottling that one can see in the Sun are the sunspots.
Sunspots appear dark because they are at a much lower temperature than
the surrounding photosphere, specifically about 1500K cooler. Recall
that the energy flux in a blackbody goes like temperature to the
fourth power, so a small change in temperature amounts to a substantial
reduction in the emitted flux or
brightness. Hence sunspots are dark. Sunspots are
believed to be caused by powerful magnetic fields poking up through
the Sun's surface. Sunspots follow something known as the solar cycle
so that there are periods of maximum sunspot activity every 11 years.
The causes of the sunspot cycle are not well understood.
Above the photosphere lies a region called the chromosphere. It
has this name because this layer of the Sun's atmosphere can be seen
during the last moments before totality in a solar eclipse as a pinkish
layer (hence color, or chromo). The pink is due to the red emission line of
hydrogen (the so-called "Balmer" line). The chromosphere is about
2000 km thick. Although it has a lower density than the photosphere,
the chromosphere has a higher temperature. Indeed from the base to the
top of the chromosphere the temperature increases to about 100,000
degrees. The chromosphere also features spike-like jets of gas called
spicules that can stick up as much as 10,000 km above the photosphere.
Finally the outermost layer of the Sun is the corona, a region of
diffuse glowing gas which can only be seen from Earth when the much
brighter glare from the Sun is blocked by a solar eclipse. (The corona
can be studied all the time by satellites in space through the use of
an obscuring disk to block out the Sun and make an artificial
eclipse.) The corona extends for as much as a million km around the
Sun and has temperatures as high as two million degrees. In fact some
regions of the corona are sufficiently hot that they give off X-rays.
The corona interacts with many of the more dynamic aspects of the solar
atmosphere. Examples include prominences, which are great arcs of gas
that extend outwards from the Sun, and solar flares which are great
explosions and jets of gas from the solar surface. All these
contribute to solar activity which is tied in somehow with the sunspot
cycle.
The Solar Interior
The only visible layers of the Sun are the photosphere and the solar
atmosphere. How is it possible for astronomers to develop an
understanding for the nature of the interior of the Sun? They
do it by using the known laws of physics and the limited amount of
information that we have measured directly from the Sun, namely its
mass, radius, composition, surface temperature, and luminosity.
Two more observations help us with our effort to model the Sun. The
first is that the Sun appears to have a constant radius; it is neither
expanding nor contracting. Since the Sun is a ball of hot gas wouldn't
you expect it to expand outward into space? Yes, if there were
no other force acting on that gas. The other force is the force of
gravity which is pulling the gas together. The Sun is in a state of
balance between the pressure forces of the gas and the gravitational
force due to the Sun's mass. This balance is called hydrostatic
equilibrium. Now pressure is a force per unit area; you exert
pressure on a wall if you put your hand on it and push. That pressure
force is exerted only over the surface area covered by your hand.
Pressure produces a net force, which in turn means a net acceleration
(from Newton's laws of motion) only if it is not in balance with some
other force. Isometric exercises are an example of force per unit area
in balance. Another example is provided by differences in water or air
pressure. At great depths the pressure of water would crush a scuba
diver's lungs if they contained only the air pressure
corresponding to the surface. Scuba gear provides air at the same
pressure as the surrounding water, which allows one to breathe.
The force of the interior air pressure
plus the forces exerted by the walls of the lungs are in
balance with the sea water pressure. There is
no net force on the lungs. Now back to the Sun. Gravity is
pulling the mass of the Sun downward. In order for pressure to
counterbalance that force the pressure at the center of the Sun must be
very large and decreasing as one goes outward through the Sun. So the
concept of hydrostatic equilibrium allows us to predict immediately
that the Sun has a high pressure center.
The next fact that we will use is that the Sun is radiating away a
great deal of luminosity but remains at a constant temperature and
constant luminosity. Since energy is flowing out from the Sun and
it is not cooling off, energy must be generated somewhere inside the
Sun. Since the Sun is not heating up that energy generation rate must
be equal to the Sun's luminosity. This is the concept of thermal equilibrium.
The source of the Sun's energy was a mystery for many years. Evidence
found on the Earth suggested (what was then regarded as) a tremendously
old age for the Earth. Fossil algae and bacteria were dated at ages in
excess of a billion years. This meant that the Sun must have been
burning much as it is today for at least as long. If the Sun were
burning by chemical reactions it wouldn't last more than a few thousand
years. The most reasonable (incorrect) answer was that the Sun's
luminosity came from gravitational contraction. If the Sun were
slightly out of balance so that gravity was pulling it into a smaller
and smaller ball, then the gas composing of the Sun would be compressed
to ever increasing densities. When you compress a gas it heats up.
For the Sun that heat could radiate away as the Sun's luminosity.
However, the entire energy available from such a gravitational energy
would power the Sun for only 30 million years. This is a lot longer
than chemical reactions but still too short for the age of the Earth.
The correct answer was arrived at in the twentieth century. The first
step was the development of Einstein's theory of relativity which
showed the equivalence of mass and energy (as generally stated in his
famous equation E=mc2). Given this equivalence one can then
imagine that it might be possible to convert mass directly to energy
(through some means). For example, given that the mass of the Sun is 2
x 1033 grams and the speed of light is 3 × 1010
cm/sec, then we find that the equivalent energy for the entire mass of
the Sun is 1.8 × 1054 ergs (= gm (cm/sec)2).
Since the Sun's luminosity is 4 × 1033 ergs/sec this gives a
possible lifetime of 4.5 × 1020 sec, which is 14 thousand
billion years. This at least allows the possibility of having a Sun as
old as the Earth!
In fact the Sun is not converting all its mass directly into energy.
The only known mechanism to convert mass completely into energy is
through matter/antimatter annihilation and this is ruled out because
the Sun is composed entirely of matter. Instead the Sun uses the
mechanism of nuclear fusion
wherein atoms of a light element (in
this case hydrogen) are joined together to form a heavier element
(helium). In the Sun the predominate energy generation mechanism is
the fusion of four hydrogen atoms into one helium atom. In this
process a small amount of the total mass (0.7%) is converted into
energy.
The process of nuclear fusion is related to but different from the
process of nuclear fission
wherein large atoms are broken apart and the
resulting pieces have less mass than the original atom. Nuclear
fission occurs (for example) when uranium atoms split apart. Nuclear
fission powers nuclear reactors and atom bombs. Controlled nuclear
fusion reactors do not exist at this time although they remain the
subject of considerable research. Uncontrolled nuclear fusion reactors
do exist: they are called H-bombs, or thermonuclear weapons. To give
you some idea of the power of E=mc2 if we consider your basic 10
megaton nuclear explosion (pictured), the energy given off (10 megatons)
represents the energy found in 47 grams of matter (about one and a
two thirds ounces). This would be produced through
the fusion of just under 7 kilograms of hydrogen.
Although it would perhaps be better if humanity left fusion to the Sun,
considerable research into it has been done (as you might suspect), and
this has coincidentally led to a better understanding of the interior
of the Sun and other stars. The main point is that in order to force
atoms to fuse into new atoms one needs to overcome the electrical
forces of the nucleus. Atomic nuclei have positive charges from the
protons in them and since like charges repel each other, it is
difficult to force
two protons together. Doing so requires considerable energy, that is
high temperatures. On Earth in order to get H-bombs to work one has
to set off an A-bomb to generate the millions of degrees of
temperature necessary for fusion (such A-bombs are euphemistically
known as "triggers.") In the Sun, such temperatures come naturally
but only at the Sun's core. Hence we expect that the energy
generation process in the Sun takes place only in its very center.
The temperatures in the center of the Sun are in excess of 10 million
degrees and the densities go as high as 160 gm/cc.
The fusion process that the Sun uses is known as hydrogen burning
by the proton-proton chain because
it depends on a reaction that combines two protons into one deuterium
atom. One proton is the nucleus of a hydrogen atom. A deuterium atom
is "heavy hydrogen" which is composed of one proton and one neutron.
The reaction is
1H + 1H ---> 2H + e+ +
neutrino
where the symbols stand for Hydrogen with one proton (1H),
hydrogen with a proton and a neutron (2H), also known as
deuterium, a positron (e+) which is the positively charged
antimatter form of an electron, and a neutrino. This reaction proceeds
at a rather slow pace; it depends on turning a proton into a neutron
and this is a reaction with a very slow rate (it involves the so-called
weak nuclear force). The positron annihilates with an electron
producing some energy, and the neutrino escapes from the Sun with no
further interaction. Neutrinos have a very difficult time interacting
with anything so in the Sun the neutrinos generated by nuclear
reactions represent an energy loss. Anyway, as the deuterium atoms are
produced they can react with protons (ordinary hydrogen) to produce
helium 3 which is two protons and one neutron, thusly
1H + 2H ---> 3He + gamma ray
Energy is carried off by the gamma ray photon. When enough Helium
3 atoms have accumulated they can combine to form one Helium 4
(which is what we regard as ordinary Helium) plus two protons
(hydrogen)
3He + 3He ---> 4He + 1H
+ 1H
The net reaction is four hydrogens turn into one Helium plus a
two positrons, two neutrinos, and some energy in the form of two
gamma rays and high speed motion in the reaction products.
Later on in our study of stars we will discuss other types of nuclear
fusion.
FIGURE: The proton-proton chain illustrated. Protons are grey
spheres, neutrons black spheres, the positron and neutrion labeled
little black spheres.
The energy released by these nuclear reactions must make its way
out through the Sun from the core to the surface through the process
known generically as energy transport. Everyone is instictively
aware of this process in terms of heat flowing from hot things to cold
things. Specifically this means that energy is moving from regions of
high energy to regions of low energy, and temperature is a measure of
the average energy. There are three main processes by which energy is
transported: Conduction, Convection and Radiation. Let's consider
radiation transport first. Radiation transport is heat transport by
photons (light). We discussed this briefly when we mentioned that a
blackbody at a higher temperature than its surroundings would send out
photons to those surroundings and eventually cool down to a temperature
equal to the surroundings (if not continually supplied with new heat
from some energy source). Radiant heat is the heat you feel coming off
from a glowing fire, or the heat you feel while standing in the Sun.
In both cases you are absorbing photons coming to you from a source at
high temperature. (Note: to protect yourself from radiant heating, you
should surround yourself with nonabsorbing, i.e., reflective material.
Fire protection suits are made of shiny reflective material.) In the
Sun photons are produced in great abundance in the core. These photons
then diffuse outward from the center of the Sun to the surface
where they escape into space. The photons do not simply stream
outward. They are scattered by the dense gas in the Sun and so must
work their way outward by a series of random scatterings. The
scattering is mostly off of electrons in the gas that have been
stripped off of the atoms by the high temperature (an ionized gas known
as a plasma). This "resistance" to the free travel of photons
through the gas is called opacity,
as in opaque. The higher the opacity of the material, the harder it is
for light to move through it. (Example: dry air has a very low
opacity, and light travels a long way through it before being
scattered. Hence you can see a long way through the air. Air
containing water droplets, i.e. fog, has a much larger opacity. Light
is scattered after a relatively short distance. Imagine the interior
of the Sun like a bright, hot, dense fog of plasma.) It takes about
100,000 years for photons to work their way out from the center of the
Sun to the surface.
Another heat transport mechanism is conduction. In conduction heat is
carried not by photons but by other particles, most often by fast
moving electrons. Suppose you have a lump of hot material which has
electrons jiggling very rapidly about within that material. You place
it next to a cold lump which has slow moving electrons. The fast
moving electrons at the interface between these two materials collide
with some of colder slow moving material and this collision exchanges
energy. The cold material starts to move faster and the hot material a
little slower. The electron collisions are trying to even things out.
You will be familiar with conduction as a heat transport mechanism
because it is what makes some material hard to touch when hot and other
materials easy to touch. As you know, metals heat up fast and transmit
heat fast. This is because they have lots of electrons that can move
easily about within the metal. This is the same reason that the
conduct electricity well. Conductors of electricity will also conduct
heat. Similarly electrical insulators are often good heat insulators.
You may have copper cooking pans but the handles are composed of
insulating plastic. Even if a good insulating material is at high
temperature you can handle it briefly because the rate of heat exchange
between you and that material is very slow. This, by the way, is the
secret to walking on glowing coals with your bare feet. But woe unto
anyone who walks on glowing metal. Anyway it turns out that the Sun is
not a particularly good conductor of heat, at least compared to
radiative transport by photons. It is a general rule that things will
always use the most efficient and fastest mechanism to transport heat
in an attempt to come into temperature equilibrium. So in stars, so
long as radiative transport is more efficient than conduction,
conduction effects will be negligible. There is a certain class of
star where conduction is important but we will delay that discussion
until later.
The last major heat transport mechanism is convection. Convection is
the physical transport of heat by moving large blobs of hot material
from the hot region to the cold region. (If you carry a bucket of hot
water along you are physically transporting heat.) In a star
convection occurs whenever there is a tendency for hot material to
rise and cold material to sink. What is required is that the hot gas
is less dense than the cold material and so weighs less than the cold
gas. This produces an overturning and circulation in the gas. A good
example is the hot air balloon. If you heat the air in a hot air
balloon then that air will be less dense than the cold surrounding air
that the balloon has displayed. The balloon will be buoyant and will
rise up through the atmosphere. This is a particular manifestation of
the general rule for the atmosphere that most people are familiar with:
hot air rises and cold air sinks. Another example is the phenomenon
of boiling water. The hot water at the bottom of the pot rises up to
the top and the cold water sinks. In this way heat from the bottom of
the pot is transported rapidly up to the top of the pot. Convection
is a very efficient means of heat transport. Think how rapidly
boiling stops if you remove a pot from the stove (its source of heat).
In the Sun convection is also an important process. Convection
becomes important whenever the opacity goes up and the rate of
radiative diffusion becomes less. Then heat builds up and the boiling
begins. Radiative diffusion is most important in the inner 80% of the
Sun, convection in the outer 20%.
All the concepts we have been discussing can be expressed in terms of
mathematical equations. Collectively these are known as the equations
of stellar structure. These include: (1) The force balance equation
for hydrostatic equilibrium. In this equation the gas pressure
forces, which are determined by the density and temperature of the
gas, are in balance with the gravitational force whose magnitude is
determined by the amount of mass inside the star. (2) Energy
conservation equation which simply says that the luminosity of the
star must be equal to the amount of energy being generated inside the
star. Energy generation is determined by the nuclear reactions inside
the star and these in turn depend upon the composition (how much
hydrogen versus helium for example), the temperature (needs to be
high) and the density (also needs to be high).
(3) The energy transport equation which says how rapidly energy
(heat) can be transported through the star at any one moment.
As we have discussed, the rate of energy transport depends on such
things as the gas opacity which in turn depends on density and
pressure. (4) Mass conservation equation: when you have calculated
your way to the surface of the star you had better have a total mass
that is equal to the mass of the star. In the case of the Sun this is
one solar mass Mo.
Given these equations the astronomer programs a computer and then works
towards a solution to the each of the equations subject to the
condition that the solar model must have the same luminosity, mass,
radius, and surface temperature as the Sun (it wouldn't be a very good
model otherwise). The outcome is data giving the temperature, density,
pressure, luminosity, etc. at every radius throughout the Sun. Solar
models tell us that the Sun generates almost all of its energy in its
core, the inner 20% of its radius. Most of the mass is contained in
the inner 60% of the radius. The upper 20% consists of the
convective zone which serves to transport the inner heat out to the
surface of the Sun.
FIGURE: A cross-section of the Sun. The major sections are the
core, where nuclear reactions occur, the radiative transport zone and
the convective zone. The convective zone reaches out to the
photosphere where the photons finally escape and fly out into space.
The photosphere is what we see as the surface of the Sun.
Just how certain are astronomers as to the accuracy of their solar
models? There are many things that need to be understood accurately in
order to get a good model. The biggest challenges are: (1) accurate
nuclear reaction rates: how fast do the energy-generating nuclear
reactions take place given a certain density, temperature and
composition? (2) accurate opacities: how do photons interact with gas
at a certain temperature and density? (3) How does convection work in
detail? How can you accurately describe regions of hot, overturning,
boiling gas? How fast does it transport energy? How fast does it
mix? Obviously if you get some of this wrong you can get a wrong
model. For example suppose you find that nuclear reactions occur a
little faster than you previously thought. This means that you could
get the same energy generation from a smaller temperature and density
in the core of the Sun. But if the density and temperature are smaller
then the size and mass of the solar model would have to change too.
The model might have the same mass as the Sun but a larger radius
perhaps. Or perhaps it would have the same radius but a more condensed
core with a larger percentage of the solar radius in the low pressure,
low density convective envelope. We will later be talking about a
whole variety of stars that have different masses, luminosities,
radii, and internal structures. For all these different stars models
have been developed to understand their interiors and their
evolution.
Must we solely rely on models to gain understanding of the center of
the Sun?
As mentioned earlier there is no way to look into the center of the
Sun using light. But the neutrinos
that are released by the nuclear
reactions in the Sun pass right through the Sun and emerge
immediately. This is because neutrinos have a very hard time
interacting with anything so they stream through matter as if it
weren't there. If we could nevertheless detect some of
those neutrinos we would be
detecting something from the very heart of the Sun. However, the same
property that allows the neutrinos to escape from the Sun means that
they are very difficult to detect (detecting something means that you
made it interact with something to produce a measurable response).
The solar neutrino experiment of astronomer Ray Davis is based upon the
fact that neutrinos can interact with a chlorine atom to become an
argon atom. The odds of that interaction occurring are very small but
if you have a large number of chlorine atoms and a huge number of
neutrinos passing through then you might expect to get an event every
now and then. The experiment consists of a 100,000 gallon tank of
cleaning fluid (which contains chlorine) in a mine in South Dakota.
The tank is down in the mine to help shield it from cosmic rays. The
mile of rock overhead doesn't represent an obstacle for the neutrinos.
From the solar models and the expected rate for the neutrino-chlorine
interaction we can predict that the tank will see one argon atom
produced every day. About every month the tank is purged of its argon
and the total amount of argon is measured. Notice that this is not an
easy experiment. We are talking about extracting something like 30
atoms of argon from 100,000 gallons of cleaning fluid. Despite the
difficulties neutrinos have been detected over the experiments long run
(it has been going since the late 60's). However, the number of
neutrinos detected is only one-third the amount predicted. What does
this mean? Could there be problems with the equations of stellar
structure, or the values of the nuclear reaction rates? Is there
something about neutrinos that we don't understand? Are the Sun's
nuclear reactions reduced for some reason? Is there new physics we
haven't included in our models?
Additional clues are expected from the operation of new neutrino
detectors. These are based not on chlorine but on the element gallium
and are considerably more sensitive than the chlorine experiment which
is only able to detect the most energetic neutrinos. However,
preliminary results are more or less consistent with Davis's result,
namely that there are fewer neutrinos detected than expected from the
theoretical calculations. At the present time physicists believe the
most probably explanation lies in the properties of the neutrinos
rather than those of the Sun. However, the experiments continue to
operate and in the next few years astronomers hope that the situation
will be further clarified.
Copyright
© 1999 John F. Hawley. All rights reserved. These notes are
intended for the private, noncommercial use of students enrolled in
Astronomy 124 at the University of Virginia. Reproduction,
distribution, and commercial uses are prohibited.