The Sun and Stellar Structure
The Sun and Its Structure
This set of notes by Nick Strobel covers: The Sun, interiors of stars, and
nuclear fusion. Parts of these notes will be in outline form to aid in
distinguishing various concepts. As a way to condense the text down I'll
often use phrases instead of complete sentences. The vocabulary terms are
italicized.
-
- Biggest thing in solar system! (1,392,000 km diameter = 109 Earth
diameters = 9.7 Jupiter diameters). Most massive thing in solar system! (333,000
Earth masses = 1046 Jupiter masses).
-
- Spectroscopy shows that Hydrogen makes up
of the solar
material,
Helium makes up 
of the sun, and all the other elements make up 0.13% (with
Oxygen, Carbon, and Nitrogen the three most abundant ``metals''-they make up
0.11%). In astronomy, any atom heavier than Helium is called a ``metal''.
Traces of Neon, Sodium, Magnesium, Aluminum, Silicon, Phosphorus,
Sulfur, Potassium, and Iron. These percentages are by relative number of
atoms. If use percentage by mass: H-78.5%, He-19.7%, O-0.86%,
C-0.4%, Fe-0.14%, rest-0.54%.
-
- Sun's Structure
- Core--innermost 10% of the Sun's mass. Where energy is generated.
16 million degrees and densities = 160
g/cm
(compare with Iron = 7
g/cm).
- Radiative zone--includes core. Energy is transported from the
superhot interior to the colder outer layers by photons. Makes up
sun's radius.
- Convective zone--outer 15% of sun's radius. At cooler
temperatures, more ions are able to block photon radiation more effectively, so
nature kicks in convection to help energy transport.
- Photosphere--``surface'' of sun. Is dense enough gas that we can't
see through it and it gives off continuous radiation. About 5800 Kelvin.
- a.
- Ways of measuring temperature:
- b.
- Features on photosphere:
- i.
- Sunspots--cooler regions on sun (1000-1500 K cooler) so don't
emit as much light
darker. Last few days to few months
map rotation of
sun (first done by Galileo). Find solar equator
rotates every 25 days while 30 degrees latitude takes 26.5 days and 60 degrees
takes 30
days. Regions of strong magnetic field. Number of sunspots varies over 11 year
cycle. At start of cycle (when #sunspots is minimum) most sunspots
degrees from
solar equator. At solar maximum (#sunspots is maximum) most
sunspots 
degrees from solar equator. In one 11 yr cycle the leading sunspot in a
sunspot group will have N magnetic pole while trailing sunspot will have S
magnetic pole. The next 11 yr cycle the poles will switch
22 yr
cycle.
- ii.
- Granulation--bright spots of convection 700-1000 km across
forming honeycomb pattern. Hot rising gas in middle of granule and cooler
falling gas on border (convection). One granule can last about 8 minutes.
- Chromosphere--pinkish outer layer 2000-3000 km thick. Since the
temperature rises outward, we see emission lines (mostly H
line at
which is red).
- Corona--very high temperature: 1-2 million degrees Kelvin! But very low density so it has a low amount of heat. Pearly white color seen in
eclipses.
- a.
- At high enough temps. the atoms collide with each other with enough
energy to eject electrons (ionization). At very high temps., things like
Iron can have 9-13 electron ejected. Nine times ionized Iron only produced at
temps. =
K.
Also see 13 times ionized Iron
(
K!).
During strong solar activity (see below) we see 14 times
ionized Calcium
(
K!).
- b.
- Most of corona trapped close to sun by magnetic field line loops. In
X-rays, those regions appear bright. Some magnetic field lines do not loop back
to sun-in X-rays see ``coronal holes''.
- c.
- Solar wind--high temps.
fast moving
ions escape sun's gravitational attraction and move outward at 100's km/sec.
Positive and negative charges spiral around magnetic field lines. When charged particles
get near a planet with a magnetic field (e.g., the Earth), some of them are
deflected around the planet and some are deflected to
the planet's magnetic poles. When the charged particles hit the planet's
atmosphere, they make the gas particles in the atmosphere produce emission
spectra--the aurora borealis in the
north and aurora australis in the south. Red aurorae produced by
Hydrogren emission and green aurorae produced by Oxygen emission. The effects
of the solar wind on the Earth is described more fully in the
Space Weather page at
Rice University (Houston, TX).
- d.
- What creates the high temperatures in the corona and chromosphere?
Possibilities: sound shock waves and magnetic loops.
-
- Solar Activity--varies with 11 yr sunspot cycle. At solar maximum there
are more sunspots, prominences, flares, and aurorae on the Earth.
- Prominences--bright clouds of corona gas forming over sunspots
magnetic connection.
Quiet ones
km
high, corona gas falling back to photosphere. Sometimes
see them looking like loops (remember that magnetic field lines loop). Last few
months to one year. ``Surge'' ones have material erupting from photosphere
shooting material up to 300,000 km above photosphere. Move along magnetic field
lines.
- Solar flares--even more extreme than surge prominences. Last only few
minutes-hours. Lots of ions ejected. Interfere with radio communication.
Sometimes cause voltage pulses/surges in power and telephone lines.
The Sun produces a lot of light every second and it has been doing that for
billions of years. How does it or any other star produce so much energy for
so long? This section will try to explain it to you.
The first basic question about the sun is what powers it? It puts
out A LOT of energy every second. How much? That's a good question. The
answer from our measurements is
ergs per sec.
An erg is unit of energy about equal to one flea hop. Since most people don't have
a grasp of flea hop energy, I'll put the sun's total energy output (ie., its
luminosity) in more familiar units. It is equal to
five Megawatt
power plants (nuclear or hydroelectric) on the Earth.
Our largest power plants now can produce around 5,000 Megawatts of power.
Another
way to look at this is that the sun puts out every second the same
amount of
energy as 
of those five Megawatt power plants would put out every year.
That's over two trillion-numbers like that on the Earth only come up
when talking about the national debt!
I know that you are just dying to know what powers that huge output, so I won't
keep you in suspense any longer. Let's first rule out other likely candidates.
How about chemical reactions? The most efficient chemical reaction is combining
two Hydrogens to one Oxygen to make a water molecule plus some energy. Such a
reaction has a very small efficiency (something like 1/10000000 of one percent).
The efficiency means the net amount of energy I get out from the reaction after
I've expended energy getting the reaction to happen in the first place.
To find out how long the sun would last
we would need to find out how much energy the sun has stored in its account
and know how fast it makes withdrawals on its account. The amount of time it
would last would be the energy stored divided by the rate of withdrawal. Makes
sense, yes? The water reaction would only power the sun for about 10,000 years.
We need a reaction with a higher efficiency. How about the ultimate in
efficiency-a matter-antimatter reaction with 100% efficiency. Such a
reaction
could power the sun for
years.
Unfortunately, there are problems with
this because the number of heavy particles in the sun must stay the same and
very soon the matter-antimatter reaction would violate that rule and nature
would not go for it.
How about gravitational settling? This is a fancy way of referring to the
converting of the potential energy of the falling layers to kinetic energy.
When you hold a rock above the
ground it has stored energy (``potential energy''--it has the potential to do
some work). The stored energy is released as you let it fall. The rock gets
kinetic
energy because it is moving. Kinetic energy can heat things up. This is what
would happen to the layers of the sun if they were to fall inward toward the
center of the sun. The gas would be compressed and, therefore, would heat up.
In addition to the expected heating the gas would also radiate. This was the
idea physicists strongly argued for until the beginning of this century. This
gravitational energy (with an efficiency of 1/10000 of one percent)
could power the sun for 
years--a nice long time except for the
nagging but ever louder criticism of the biologists who needed more time for
evolution to occur and the geologists who preferred the idea of unlimited age
for the Earth but would stomach something like a few billion years for the age
of the Earth. A good article on the age-of-the-Earth debate is in Scientific
American August 1989 pages 90-96. Eventually physicists had to change their
minds about the age of the sun (and Earth) as radioactive dating (something
physicists believe is correct) indicated a 4.6 billion year age for the solar
system and, therefore, the sun. It was the fact that the sun could not last
long enough being powered by gravitational contraction or settling that
motivated the search for nuclear power sources.
We are left with nuclear power as the only thing left to power the sun.
There are two types possible: fusion
and fission. Fission produces energy by breaking up massive particles
like
uranium into less massive particles like Helium and Lead. Fusion produces
energy by fusing together light particles like Hydrogen into more massive
particles like Helium. Atomic power plants and the Atom Bomb use fission
to get the energy. Stars and Hydrogen bombs use fusion. To get positively
charged particles to fuse together, the electrical repulsion must be overcome
(remember that like charges repel and opposite charges attract-something that
rarely happens in human interactions). Once the positively charged particles
are close enough together (within several
centimeters of
each other),
the strong nuclear force takes over and is much more powerful than the electric
force. The nuclei stick together. To get those particles close enough together
requires high temperatures and high densities-something that occurs naturally
in the cores of stars.
Fusion takes light particles whose combined mass is more than the
resulting fused massive particle. The mass that was given up to form the
massive particle was converted to energy. Remember
? That
tells you how much energy (
)
can be made from matter with mass 
.
Remember that 
is the speed of light and it's squared (!) so a little bit of mass can make a
lot of energy. An example for fusion
is the fusion process in the cores of main-sequence stars that takes four
Hydrogen
nuclei (protons) each with mass of one proton and fuses them to form a Helium
nucleus (two protons and two neutrons) that
has the mass of 3.97 times the mass of one proton. An amount of mass equal to
0.03 times the mass of one proton was given up and converted to energy
equal to
.
The efficiency of this reaction is about 4/5 of one percent.
The sun could last for about 10 billion years on hydrogen fusion
in its core. This is plenty long enough to satisfy the modern geologists.
The next basic question is why does nature use the long complicated
proton-proton chain (or the longer Carbon-Nitrogen-Oxygen chain) for fusion?
Nature uses a three step chain process to fuse four protons to make one Helium
nucleus for the proton-proton chain process.
Wouldn't it be much simpler if four protons would collide simultaneously to
make one
Helium nucleus? Simpler, but not very likely is the answer. Getting four
objects to collide simultaneously is very hard to do-the chances of this
happening are very very small (as one from a family of 8 boys I can attest to
the difficulty of getting just half of us together for a mini family reunion!).
The chances of this type of collision are too small to power the sun, so nature
has found a trickier scheme. The chances of two particles colliding and fusing
is much higher, so nature slowly builds up the Helium nucleus.
Nuclear fusion is something of a holy grail for utility companies
because it produces no nasty waste products and has the potential of getting
more energy out of it than you put in-free energy! Unfortunately, the
conditions to get fusion to happen are very extreme by our standards. We've
been only able to tap the fusion process with the Hydrogen bomb, but that's
a one shot deal. The Hydrogen bomb still needs an atomic bomb trigger to get
the extreme temperatures needed for the fusion process. At least
we can get the waste product of the sun's fusion process for free with solar
power collectors. The sun can have a controlled fusion
process and not blow up all at once because of the hydrostatic equilibrium
``thermostat''.
Hydrostatic equilibrium is the balance between the thermal
pressures from the heat source pushing outwards and gravity trying to make the
star collapse to the very center. I'll discuss hydrostatic
equilibrium in
more depth (no pun intended) in the next section. The nuclear fusion rate is
very sensitive to
temperature. It increases as roughly
for the proton-proton
chain and even more sharply (
)
for the Carbon-Nitrogen-Oxygen chain. So a slight increase in the temperature
causes the fusion rate to increase by a large amount and a slight decrease in
the temperature causes a large decrease in the fusion rate.
Now suppose the nuclear fusion rate speeds
up for some reason. Then the following sequence of events would happen:
1) Thermal pressure would increase causing the star to expand; 2) Star would
expand to new point where gravity would balance the thermal pressure; 3) but
Expansion lowers temperature in core-nuclear fusion rate slows down; 4)
Thermal pressure drops and star shrinks; 5) Temperature rises and nuclear
fusion rate increases; 6) Stability between nuclear reaction rates and gravity.
A similar type of scheme would occur if the nuclear fusion rate were to slow
down for some reason. The fusion rate stays approximately constant for stars
that are fusing hydrogen to make helium + energy in the core. Once the hydrogen
fuel in the core has been used up, hydrostatic equilibrium can no longer
stabilize the star. What happens next will have to wait until we talk about
stellar evolution.
Here's a summary of fusion in outline form along with some discussion of a
particle produced from fusion-the neutrino.
-
- Need energy source that lasts long time. Nuclear
Fusion-lighter nuclei fuse together to form heavier nucleus + energy.
The sum of the light nuclei masses = heavy nucleus mass +
energy/c
(remember ).
The ``c'' is the symbol for the speed of light.
-
- Use chain process to fuse Hydrogen to Helium. Chain process much more
probable than all at once process. Proton-Proton chain and
Carbon-Nitrogen-Oxygen chain process.
-
- Sensitive to mass. More mass
more
reactions. Main sequence type stars-hydrogen fusion powered.
-
- Neutrino--massless (nearly??) particle traveling at speed of
light
(close to??) produced in nuclear reactions. More reactionsmore neutrinos.
Hardly interact with matter (low probability of interaction). Pass directly from core to us. Billions pass through us every second. If we could catch
neutrinos,
we could find out what it's like in Sun's interior just 8 1/3 minutes ago. The photons of light produced in the core take about a million years to
percolate out to the surface. Increase odds of easy detection of a few neutrinos by using a LARGE amount of material that reacts with neutrinos in a certain way
(Chlorine changes to radioactive Argon, Gallium and water molecules give off
flashes of light).
-
- Solar Neutrino Problem--we get only 1/3 the expected number of
neutrinos! Possible reasons:
- Fusion is not sun's power source (not supported by other observations).
- Experiments not calibrated correctly (unlikely that all the carefully
tuned apparati tuned in the same wrong way).
- Nuclear reaction rate lower than what our calculations say (possible but
many people have checked and re-checked the physics of the reaction rates).
- Neutrinos change into other types of neutrinos that don't interact with
the detection material during flight from Sun to Earth (idea gaining more and
more advocates). Requires neutrino to have some mass. If the neutrino has mass,
then it cannot travel at the speed of light, but can get darn close. Also a
neutrino with mass has important consequences for the evolution of the universe
(more about that later).
This section is about how we find out what the interior of a star is like
without physically taking one apart (a rather difficult thing to do).
-
- Use mathematical models: set of equations describing how things
work. Since interior is gaseous, the equations are simple (whew!). Three
parameters:
- Temperature--average kinetic energy of
gas particles.
- Pressure--force/area. Hot gas wants to
expand causing pressure.
Example: The gas inside a hot air balloon pushes out on the material of the
balloon enclosing the gas.
- Mass Density--mass/volume. Gas can be
compressed to smaller
volumeslarger
densities.
-
- Use Equation of State--equation relating density, pressure, and
temperature. Gas has simple one (pressure = constant
mass density
temperature /
molecular weight). For Hydrogen, the molecular weight
is very close to 1; for Helium, the molecular weight is very close to 4. For
a gas made of different types of atoms, the molecular weight is the weighted
mean of the different atomic types, taking into account their relative number
proportions.
-
- Star held together by gravity. Gravity tries to compress everything to center. What holds star up (prevents total collapse)? Thermal pressure! Thermal
pressure tries to expand star layers to infinity. In any given layer of star
there is a balance between thermal pressure (outward) and weight of material
above pressing downward (inward)--Hydrostatic Equilibrium. Deeper layers
have more gravity compression from overlying layers (density increases).
Need more pressure to balance-raise temperature. Find temperature at
core = 8-28 million deg. K and densities = 10-130
g/cm. As stars age,
these numbers increase! We've already seen in the previous section that
hydrostatic equilibrium provides a ``thermostatic control'' on the energy
generation and keeps star stable.
-
- Other pieces to the models:
- Continuity of Mass: total stellar mass = sum of
shell layer masses AND mass is distributed smoothly throughout star. Conservation of Mass: the total
amount of mass does not change with time.
- Continuity of Energy: Amount of energy flowing
out
top of shell = amount energy flowing in at bottom of shell layer AND star luminosity = sum of shell layer energies. Conservation of Energy: the total amount of energy does not change with time.
- Energy Transport: Energy moves from hot to cold via
conduction, radiation, or convection. Nature will first try using radiation. 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. For stars conduction is not
an efficient process so it transports a very small amount of energy.
- Put B, C, D together to form mathematical computer model.
-
- Takes LONG time for photon produced in core to reach surface. Opaque
interior-photon ionizes atom (photon gone), nucleus + electron(s) recombine
and photons re-emitted in random direction, photon ionizes another atom, etc.
Photon goes
cm
between ionizations. On average, photon moves outward,
taking
million years to go from the core where it was created to the surface where it
is finally released.
last updated 19 Sept 95
Nick Strobel --
Email:
strobel@astro.washington.edu
(206) 543-1979
University of Washington
Astronomy
Box 351580
Seattle, WA 98195-1580
.
So we measure a solar flux on Earth =
.
We know
--it's a
constant of nature, Earth's solar flux, and 1 A.U. so we can
solve for the temperature. Upper parts are cooler and less dense so we see
absorption lines.