Lecture 5
The Internal and Surface Structure of
the Sun
I. Internal Structure of the Sun
A. Core: inner ~1/5 solar radius where the Sun's energy production
takes place; core temperature = 15 million K, core density = 100 x density
of water, core pressure = 200 billion x surface pressure of Earth; composition
mostly hydrogen in gaseous (ionized gas = plasma) form
1. energy source: nuclear fusion (light nuclei combine to form
heaver nuclei); the overall reaction for the Sun results in 4 hydrogen
nuclei combining to form 1 helium nucleus + energy; each helium nucleus
produced is slightly less massive than the combined mass of the 4 hydrogen
nuclei (~0.7% less), this so called "mass deficit" is coverted into energy
as described in Einstein's equation: E = mc2
2. proton-proton chain = specific nuclear reaction which provides
the majority of the Sun's energy:
step 1: 1H + 1H ->2H
+ e+ + neutrino (e+ + e- ->
gamma ray photon)
step 2: 1H
+ 2H ->3He
+ gamma ray photon
step 3: 3He
+ 3He ->4He
+ 1H + 1H
Note 1: steps 1 & 2 happen twice for each step 3 reaction; bottom
line, 41H combine to form 14He
with the release of energy
Note 2: IMPORTANT: The fusion
reactions in the Sun and other stars would not be sustainable if not for a
quantum mechanical process known as "quantum tunneling". At the
energies found in the cores of stars, the protons and other nuclei involved
in the fusion reactions could not get past their mutual replusion (due to
their positive charges = "Coulomb barrier") in sufficient numbers to sustain
the nuclear reactions without this quantum effect.
3. 600 million tons of hydrogen
are converted into 596 million tons of helium every second in the
core of the Sun, the "missing" 4 million tons of mass is converted into
energy ( E = mc2 ) = 3.8 x 1026 joules every
second; in other words, the Sun has a radiant power output (luminosity)
of 3.8 x 1026 watts
4. the rate of energy production in the core depends on the temperature
and density in the core; the Sun is in hydrostatic equilibrium which
means that the pressure generated by the energy production in the core
is just balanced by the weight of the overlying layers; this "contest"
between pressure and weight (gravity) acts like a "thermostat" and controls
the rate of energy production and the overall structure of the Sun (this
is true for all stars as well) - for example: if the fusion
rate decreased slightly -> pressure
would decrease ->
gravity would cause the Sun to contract slightly ->
density
and temperature would increase in the core ->
the fusion rate would increase ->
pressure would increase and the Sun would stop contracting
B. Radiative zone: from the center of the Sun out to a position
about 1/3 the solar radius below the surface, conditions in the plasma
are stable against convection and the energy created in the core is transported
outward by photons (ie: by radiation)
1. gamma ray photons created by
the nuclear reactions in the core are scattered or absorbed and reemitted
by the particles in the plasma as they make their way through the radiative
zone; one gamma ray photon becomes many lower energy photons by the time
they reach the photosphere (total energy of the lower energy photons sum
to the energy of the original gamma ray photon)
2. the total time it takes for
the photon created in the core to complete the "random walk" process out
to the surface (described in 1. above) is on the order of one million years;
this "random walk" process is know as radiative diffusion
C. Convective zone: in the
outer ~1/3 of the solar radius, the conditions in the plasma allow for
the process of convection to transport the energy to the surface
1. convection occurs when conditions
in a fluid material are such that a parcel of the material can't lose its
heat energy to the surrounding material very quickly by conduction or radiation,
then the parcel becomes hotter than the surrounding material, becomes less
dense and begins to rise like a hot air balloon, carrying its heat energy
upwards by mass motions
2. when the material reaches the
surface it radiates away some of its heat energy and cools, sinking down
around the rising column of hot material, this is called a convection
cell and we see the top of these cells in the photosphere as solar
granulation
D. Determining the interior structure
of the Sun
1. our knowledge of the interior
structure of the Sun (for that matter, all stars) is determined mainly
by computer models which use the laws of physics and the measurable global
and surface properties to calculate the temperature, density, pressure,
energy production and even changes in composition due to nucleosynthesis
(fusion reactions) as a function of the radius
2. the measurable properties of
the Sun which we measure to calculate the interior model include:
total solar mass, average mass density, radius, total luminosity, surface
temperature, surface pressure, surface density
3. there is one direct measurement
of conditions in the core of the Sun: the neutrino flux from the
fusion reactions that occur in the core; neutrinos are subatomic particles
that only weakly interact with normal matter, a typical neutrino could
fly through 6 trillion miles of lead without being absorbed; about 2% of
all the energy produced by the solar nuclear reactions are carried off
as neutrinos; there are three different types of neutrinos
a. the solar neutrino problem:
for many years there have been devices (neutrino telescopes) that
could detect the neutrino flux from the Sun; none of these neutrino telescopes
have ever detected the number of neutrino from the Sun expected from the
standard solar model
b. recently researchers have determined
that the neutrino is NOT a massless particle (like the photon), this implies
that the neutrino can change type in flight and explains the deficit in
the neutrino count measured at neutrino telescopes; the solar neutrino
problem was caused by our incomplete understanding of the physics of neutrinos
rather than the physics of the standard solar model
II. The Surface Structure of the
Sun: the Photosphere
A. Photosphere: the visible surface of the Sun, actually the
top ~400 km of the convective zone where most of the photons escape out
into space; photosphere average temperature = 5800 K, composition of Sun
(as measured in the photosphere) = 70% hydrogen, 28% helium, 2% heaver
elements by mass, radius of Sun (to photosphere) = 696,000 km
1. limb darkening: as we observe the Sun in visible light (using
the necessary filters!) the surface brightness falls off from the center
towards the edge (limb); the light we see coming from the center of the
disk is escaping from a deeper (hotter) level in the photosphere than the
light we see from the limb; from the Stefan-Boltzmann law we know that
the power emitted per unit area is a strong function of the absolute temperature,
therefor we see brighter (more power per unit area) light from the deeper
(hotter) levels that we sample near the center of the disk than the higher
(cooler) levels that we sample near the limb
2. granulation: the photosphere is the top layer of the convective
zone and the surface expression of the convection cells are roughly hexigonal
bright patches with darker edges; the brighter center of the patch is due
to the hot upwelling column of gas and the darker rim is the cooler sinking
material; as seen from the Earth through a telescope, these ever-changing
patches give the Sun's surface a grainy appearance, hence the term granulation
B. Sunspots, the 11 year sunspot or solar activity cycle and the
22 year solar magnetic cycle
1. sunspots: cooler (4000 K) regions of intense magnetic field
strength in the photosphere that look dark compared to the surrounding
6000 K photosphere; sometimes referred to as "magnetic storms" due to the
high field strength and accompanying solar activity
2. the number of sunspots observed in the photosphere and occurances
of energtic solar activity associated with them wax and wane with a period
of approximately 11 years; at a sunspot minium there are few sunspots,
they begin to form at high solar latitudes and as the cycle progresses,
larger numbers are observered at the mid-latitudes, then as the numbers
decrease they are found closer to the equatorial region, as the cycle begins
to repeat they are again observed at high latitudes
3. sunspots activity is associated with the solar magnetic field;
sunspots appear in groups of at least 2 and each sunspot has a magnetic
polarity (ie: either a "north magnetic pole" or a "south magnetic
pole") with one polarity associated with the leading (toward the direction
of solar rotation) sunspots of the group and the other with the trailing
sunspots, whatever the polarity of the sunspot groups in the northern hemisphere,
it is reversed in the southern hemisphere (if the polarity is [-
+] to the north, then the polarity
is [+ -] to
the south; it is thought that the differential rotation of the Sun (~28
days near the equator, ~36 days near the pole) "winds" the Sun's magnetic
field as its plasma drags the magnetic field lines with it (see lecture
6 for a discussion of magnetic field lines); eventually during an 11
year sunspot cycle the process causes the Sun's global magnetic field to
reverse in polarity, the polarity reverses back again during the next 11
year cycle ending a 22 year solar magnetic cycle
C. Solar seismology and the convection zone: the churning motion
of the convection zone drives oscillations of the fluid surface of the
Sun; a standing wave pattern developes (like the vibrational pattern that
occurs on a drumhead when hit by a drumstick), this standing wave pattern
can be observed by measuring the up-and-down motions of the plasma in the
photosphere with spectrographs (see
doppler shifts) and there is a global network of telescopes for continuous
time coverage of the pattern; analysis of this pattern allows astronomers
to determine the internal rotation rate of the Sun and the distribution
of sizes of convection cells and test other models about the convection
zone