Physics 202
Intro to Astronomy:  Lecture #14
Prof. Dale E. Gary

Our Star The Sun

The Sun is a Star

All of the thousands of stars you can see at night with the naked-eye, and all of the millions you can see faintly shining in the Milky Way, are suns, similar to ours.  Our galaxy contains 100 billion suns, and most are ordinary stars very similar to our Sun.  So what we learn from studying the Sun also applies to all of these ordinary stars.  Since nearly every other star can be seen only as a mere point of light, we can see how important it is to have one star close enough to resolve and study in detail.

We went into quite some detail talking about the birth of the solar system from a collapsing cloud, examining the phenomena taking place in the outer reaches of the solar nebula, but we glossed over what was happening in the central part that ultimately became the Sun.  We will revisit these ideas again when we talk about star birth in general, but here are the main events that formed the Sun from the center of the cloud:

All stars form in basically the same way, and so all stars have the same basic structure.  The power output of the Sun, called the solar luminosity, is constant at 3.8 x 1026 watts.  This is an incredible amount of power--even at the distance of the Earth we receive 1370 watts/m2, meaning that we could power about 14 lightbulbs of 100 W each, for every square meter of area.
The Structure of the Sun
Let's take a look at the structure of the Sun starting from the outside, from Earth, and moving inward toward its center.  Here are the regions of the Sun that we will visit:
Distance from center
Solar Wind Variable >100 AU 400-800 km/s
Corona 3 million K 0.15 AU (30 Rsun) Highly dynamic loops
Chromosphere 10,000 K 2000 km above surface Filaments, Plage
Photosphere 6,000 K Surface (1 Rsun) Sunspots, Granulation
Convection Zone 100,000 to several million K 0.7 to 1 Rsun Upward and downward motions
Radiation Zone 10 million K 0.2 to 0.7 Rsun Energy carried by photons
Core 15 million K 0 to 0.2 Rsun Region of nuclear fusion

Solar Wind: Even at the distance of the Earth we can be said to be inside the Sun.  Particles and magnetic fields from the Sun make up the solar wind, which blows past the Earth at speeds from 400-800 km/s (about 1 million mph!).

Corona: The source of the solar wind is the solar corona, which is the tenuous outer atmosphere of the Sun.  The corona is very hot (several million K), and so it shines in X-rays and ultraviolet light, but also can be seen in visible light during an eclipse (it is too faint to see otherwise).  The corona is highly dynamic, and looks different every time you look at it.

TRACE image of coronal loops in the UV

Chromosphere: This is a relatively thin layer that shows as pink during a solar eclipse, hence the name chromosphere, which means color sphere.  Some of the strongest spectral lines from the Sun come from the chromosphere, and we can take pictures using the light in one of these lines.  NJIT runs the Big Bear Solar Observatory, where we can see the latest images in the hydrogen alpha line.  Here we see a number of features of the solar atmosphere, including filaments (dark clouds of hydrogen gas suspended above the surface) and prominences (same as filaments, but sticking out above the limb of the Sun) , sunspots (dark spots), and plage (bright areas around sunspots).

Photosphere: This is the visible surface of the Sun.  It is called the photosphere because this is the point of the last scattering of photons before they escape directly into space.  It has a remarkably uniform temperature of about 6000 K, except in small spots called sunspots that come and go with time.  The sunspots are regions of high magnetic field, which inhibit the flow of heat from the hotter surroundings, so they are cooler (about 4000 K).  This is why they appear dark.  In fact, they only appear dark because they are seen against the brighter, hotter surroundings.  If you could see them in isolation, they would glow brightly, and would be reddish in color.  In fact, many stars have surfaces about 4000 K or less, and they emit plenty of light.  If you look closely at the photosphere away from sunspots, you can see a fine convection pattern called granulation. Click here for a movie.

Convection Zone: Just beneath the photosphere, and extending inward to about 0.7 Rsun, is the convection zone.  Energy generated in the core of the Sun moves outward through this layer by a boiling motion in which hot plasma rises, releases some of its energy, cools, and then sinks again.  This entire layer of the Sun overturns on a timescale of months.  The convection cells in this layer are far larger than the surface granulation, and become turbulent due to the low viscosity and the rotation of the Sun.

Radiation Zone: Deeper into the Sun, the plasma suddenly becomes smoother and the turbulence disappears.  From here all the way to the core, energy is not transported by boiling motions, but directly by radiation.  The photons kind of percolate through the layer, going a short distance, interacting with an atom, changing direction, going a short distance, slowly diffusing outward in a random walk.  It takes a photon about 1 million years to traverse this layer!

The Core: The core of the Sun is where the temperature is high enough for active nuclear fusion.  That is where hydrogen, the nuclear fuel, is being converted to helium.  The core is the only place in the Sun where significant energy is being generated.

Nuclear Fusion
There are two ways to extract energy from atomic nuclei--these are nuclear fission (splitting of atoms) and nuclear fusion (combining of atoms).  These terms sound similar, but they are in fact opposite processes.  Fission usually starts with very large nuclei, like uranium-238 (238 nucleons), which can spontaneously split into two smaller atoms.  Atoms greater in mass than iron will release energy when split apart, but it takes energy to put them together.  However, atoms smaller in mass than iron will do just the opposite -- they release energy when put together (fused), and take energy to split apart!  So iron is at the top of the energy curve -- iron is the most stable because adding particles or taking particles away both require energy input.

The universe started in the big bang with the simplest of atoms -- mostly hydrogen (just a single proton) and about 10% helium (two protons and two neutrons).  So stars have only these to work with, and to get energy out of them requires fusing them together.  Luckily for stars (and for us), there is plenty of energy to get out of fusing of hydrogen to make helium.  Normally, hydrogen atoms (protons) very strongly resist being pushed together due to the fact that they have the same charge, and like charges repel.  The force that keeps them apart is the electromagnetic force.  However, if you can get two protons close enough together, suddenly they are attracted VERY strongly by a new force, called the strong force.  This is the nuclear binding force that holds all atoms together.  The trick is to get the two hydrogen atoms close together.  This can be done in the cores of stars because of two properties -- the high pressure, which means that they are close together due to collisions with their neighbors, and the high temperature, which means they are moving very fast and can collide violently.

When two protons combine, you might think you would end up with a light form of helium, but in fact what really happens is that one of the protons spits out its charge in the form of a light particle called positron (this is the antiparticle of the electron). This is the manifestation of another nuclear force, called the weak force. During this decay of the proton, an extremely tiny particle called a neutrino is also produced. We will discuss neutrinos more later--we will see that they are very important. When a proton spits out a positron it becomes a neutron, which paradoxically is slightly heavier than a proton.  The nucleus that is left behind is a heavy hydrogen nucleus with one proton and one neutron -- this is called deuterium.  This process is called a nuclear reaction.  The kind of fusion going on in the Sun involves other reactions that take place between these deuterium nuclei, to eventually result in a helium atom.  Here is an overview of the entire process.

By looking at the "total reaction" figure, you can see that ultimately 4 protons combine to make one helium nucleus, liberating energy in the form of two positrons (e+), two neutrinos, and two gamma rays (high energy photons).  The positrons quickly collide with electrons and annihilate (this is a matter-antimatter reaction), liberating more energy.  Only the neutrinos escape.  We will discuss those in a moment.

The Solar Thermostat
The fusion reactions we just described happen at just the right rate to keep the Sun from collapsing, but they are highly dependent on temperature.  If the temperature were a little cooler, the fusion reaction rate would decrease, releasing less energy.  If the temperature were a little higher, the reaction rate would increase, releasing more energy.  You might think that this is unstable--less energy means more cooling, which means less energy, etc.  Or, more energy means more heating, which means more energy, etc.  But let's look at what happens if the core of the Sun should, for some unexplained reason, get a bit hotter.  In that case, indeed the reaction rate would increase and release more energy, but at the same time the heat would cause an increase in pressure.  The upward pressure force will overbalance the downward gravity force, and the Sun would expand.  But on expanding, the pressure and temperature will do down, and the reaction rate will go back to normal, so that the Sun will come into equilibrium again.  In this way, the temperature and pressure of the core of the Sun are kept exactly in balance to counter the force of gravity.  For the Sun, the reaction rate is fairly slow, so that the hydrogen "fuel" will last about 10 billion years!  For a more massive star, though, the gravity force is much higher, so the reaction rate has to be higher to balance it.  We will see that more massive stars than the Sun live much shorter lives.
Seeing Inside the Sun
There are two methods that we have, to directly find out what the interior of the Sun is like.  The first is by means of the neutrinos that we mentioned before.  We said that photons take a million years to escape the Sun, but neutrinos are so unreactive that they escape directly.  If the Sun's core were to get cooler, we would not know it for about a million years if all we had were photons. But by measuring neutrinos we can know it nearly instantaneously.   The Nobel Prize in Physics in 2002 was awarded to Raymond Davis, who pioneered the method for detecting solar neutrinos.  Imagine the surprise when, after many years of measuring neutrino fluxes from the Sun, he found that only about 1/3 the expected number were detected.  Did this mean that we had the reaction rate wrong inside the Sun?  In 2002, the mystery was solved (in fact, our text still calls it the Solar Neutrino Problem even though it is now understood, because we just figured it out).  It has been shown that neutrinos can change from one kind to another, and about 2/3 of them change to a kind that Davis could not detect.  After correction for this effect, it turns out that the number detected agrees perfectly with our understanding of the reaction rate of the solar core.

The other way to see inside the Sun is by using "sun-quakes" or sound waves that travel through the inside of the Sun.  This is a method called helioseismology.  We do not have time to discuss it in detail, but with helioseismology we can measure the rotation rate inside the Sun, where we see that there is a discontinuity at the base of the convection zone.  We can even see sunspots on the other side of the Sun!