Sunday, August 31, 2014

What’s at the Center of the Sun?

Here is an illustration of a rocket flight from the surface of Earth to the center of the Sun. A few altitudes in each atmosphere are shown. The Earth altitudes are the surface, tropopause (where airliners fly), and the Kármán line (the boundary between our atmosphere and space). The Sun shows the photosphere (the visible surface of the Sun), the bottom of the convection zone, the top of the nuclear core, and the center of the Sun. I used atmospheres (atm) as the unit because 1 atm is the pressure we are most used to.

A question about the interior of the Sun was recently asked on the Little SDO Facebook page:

"No one will ever know what is at the core of the sun. How do the scientist know what’s at the core, have they been in there? Did they actually build something that can withstand the heat of the sun to go in there and look?"

Amazing as it seems, we know quite a bit about the conditions at the center of the Sun. They are measured in two independent ways, sound waves and neutrinos. We also build models of the Sun that use what we know about the physics of plasmas that must agree with those measurements.

Let’s think about the models first. Stars live in a state of precarious balance between gravity trying to pull material inward and pressure pushing the same stuff outward. At every altitude in an atmosphere the pressure needs to be sufficient to hold up the mass of material above it.

You live at the bottom of an atmosphere. The mass of the atmosphere above you produces a pressure at the surface of (believe it or not) 1 atmosphere! It is also a pressure of 1015 mbar or hPa. How does an atmosphere work? Think of the atmosphere as having layers that start at the ground and going toward space. If you move from the lowest level (at the ground) up to the next level we find that the pressure is smaller because the higher level supports less mass. As we continue moving up the pressure continues to decrease until finally the density is too low and we say we are in outer space.

How do we relate this to the Sun? Starting at the top of the Sun we find a small pressure is necessary to hold up the small mass of the atmosphere. Moving down into the Sun we find the pressure continues to increase until we reach the core. Pressure comes from temperature and density (remember the ideal gas law). That means the temperature and density also increases as we move into the Sun

Astronomers know how to use these models to estimate the pressure, temperature and density in the core of the Sun. The simplest models give a core temperature of 20 million K, a core density of 75 gr/cm3, and a central pressure of 1.2e17 dyne/cm2. That is a pressure of 120 billion atmospheres! Even at these incredible pressures the core of the Sun is hot enough that the material remains a gas. More accurate models that follow the fusion reactions that power the Sun give the pressure as 2.4e17 dyne/cm2 (230 billion atm), a temperature of 15.7 million K, and a density of 154 gr/cm3. The illustration shows some pressure values at some altitudes in the atmospheres of the Earth and Sun as if we could fly a rocket to the center of the Sun.

But scientists are skeptical of models and those numbers should also be checked by a measurement. This led to one of the great debates of physics, the core conditions deduced from Sun’s sound waves and the core deduced from the observed number of neutrinos, known as “Solar Neutrino Problem”.

When the velocity of the solar surface is analyzed we find that it is made up of millions of waves moving with measurable frequencies. These waves also move around inside the Sun. Roughly speaking the lower the frequency of the wave the deeper the wave moves into the Sun. We can also calculate the frequencies of the waves that move in the models we built earlier. Because there are so many waves, matching the model and observed frequencies gives a very good check on our model. (This is like tuning a large bell or pipe organ.) Our current model agrees very well with the observed frequencies. That means the sound waves confirm that the temperature and pressure at the center of the Sun agrees with the frequencies from the accurate model of the Sun.

Another check on this comes from the neutrinos that are emitted by the fusion reactions in the core of the Sun. Neutrinos are neutral particles that interact very poorly with other particles. They have very small masses and come in three flavors, electron, muon, and tau. Neutrinos are very difficult to detect but would tell us whether the reactions used in the model were correct. When they were first detected, the meaasured number of neutrinos did not agree with the model that worked so well for the waves. Less than half of the number predicted by the model were observed!

After much research, such as changing the model near the core to reduce the fusion reactions and the calculated number of neutrinos the model would emit, a new theory of neutrinos was tried. The Mikheyev-Smirnov-Wolfenstein (MSW) effect causes neutrinos to change flavor, from electron neutrino to muon or tau neutrino, as they move through matter. Could this be the reason for the “Solar Neutrino Problem”?

The first neutrino flux measurements in the Homestead Mine were of only very high energy neutrinos. Lower energy fluxes from the Sudbury Neutrino Observatory showed that most of the neutrinos produced by the fusion reactions in the core of the Sun, all of which are electron neutrinos, are changed into muon and tau neutrinos by the time they reach the Earth. Once this particle physics concept was confirmed, the central temperature of the Sun from the sound waves is confirmed.

People have thought about the center of the Sun for over 100 years. The models of the Sun are based on the 1983 Nobel Prize winning work by S. Chandrasekhar and W. A. Fowler. The 2002 Nobel Prize in Physics was awarded to R. Davis and M. Koshiba for the first detection of cosmic neutrinos. T. Duvall, a scientist who works with SDO data, recently won the AAS/SPD Hale Prize for his work using the sound waves to understand the inside of the Sun.

That’s how we know the conditions at the core of the Sun.