THE SUN: MAGNETIC PROPERTIES, SUNSPOT CYCLE

We will use the sunspot cycle to discuss SCIENTIFIC MODELS.

Sunspots and Magnetic Fields

Sunspots are not really black. They are actually very bright, but the photosphere is so much brighter that there is the optical illusion that sunspots appear dark.

The anatomy of sunspots: The umbra is the center of the sunspot. The penumbra is the transition from the photosphere to the umbra. Sunspots have temperatures of typically 3000-4000 degrees K. Sunspots have very strong magnetic fields, this is known because in the spectrum of a sunspot, the absorption lines are seen to separate in wavelength, or "split". This line splitting is because atoms behave a bit differently in strong magnetic fields. It is called Zeeman splitting.

Sunspots arise because strong magnetic fields that happen to concentrate on the sun's surface suppress convection. That is, they stop hot gas from rising to the photosphere. This is because electrically charged particles get locked onto magnetic field lines. The particles spiral around the field lines. Thus, their free movement is suppressed. This is what suppresses the upward convection of hot material and resultd in a cooler zone on the photosphere, i.e., a sunspot.

Solar prominances are also confined by magnetic fields. The charged particles move along the field lines (they are trapped to go in the direction of the magnetic field). Thus, the shape of a solar prominance directly shows the shape of the magnetic field (giving them the characteristic horse shoe shape).

The Sunspot Cycle and Other Data

Sunspots come in an 11 year cycle. The Maunder Butterfly diagram shows how during this cycle. The sunspot cycle starts at mid-latitudes (away from the solar equator) and then with time through the cycle, sunspots mostly appear near the equator. It is a diagram of latitude versus time.

The sun does not rotate like a solid body. The equator rotates slightly faster than the mid latitudes. The sun rotates about once per month, but the equator make one rotation about three days before the mid-latitudes make one rotation. This is called differential rotation.

Sunspots have four peculiar properties.

• they always arise in pairs very close to each other (they are usually separated by the size of a few sunspots from each other).
• in a given pair, one spot has magnetic north polarity, and the other member of the pair has magnetic south polarity. Together, it is as if they form a magnet.
• the pairs are always aligned in the direction of rotation (always east-west), and never perpendicular to the rotation (never north-south).
• In each hemisphere of the sun, the polarity of the "leading" sunspot is opposite.

All facts about sun spots are summarized on one slide of the Notes. This is a lot of information, which you do not need to memerize, but which we would like to make some sense of. So, we formulate a scientific model based upon the hypothesis driven scientific method to attempt a physical picture of what is happening in the sun. This model should be able to explain as much of the data as possible, but it may not explain all of it. It should also make additional predictions, which will serve as a test. It the predictions fail, then the model needs to be significantly revized. If the predictions hold to be true, then we can make minor refinements and build upon the model.

Hypothesis Driven Science

The scientific method is a creative process of discovery. It begins with an observation.

• The creative part then is the process in which a person, or observer, formulates a question about Nature based upon the observation.
• The question leads to a hypothesis. A hypothesis is an educated guess about how a particular phenomonon behaves. The hypothesis is also a creative step.
• Using logic, then a prediction is made based upon the hypothesis. This also requires creative thinking.
• Then, a test is created (creative process), to test the prediction of the hypothesis. The test is usually an additional observation, but under controlled circumstances.

There are two outcomes to the test. (Case 1) the predicted behavior is NOT observed; the hypothesis is proved wrong. (Case 2) the predicted behavior is observed; the hypothesis is NOT proved wrong.

Can you ever prove your hypothesis is corrcet?

A hypothesis can never be proved correct, only proved wrong. If the hypothesis is proved wrong, this is usually a very clear result from the test. And once it is wrong, that is it- game over for our hypothesis. If the result of a test is that the hypothesis is correct... then have we proved the correctness of our hypothesis? No.

What if we run the test 1000 times and the hypothesis is correct all 1000 times?... then have we proved the correctness of our hypothesis? Still No. Let's say some condition that we were not aware of changed from test 1000 to test 1001 and then the hypothesis now tested false. Well, game over for the hypothesis. And, we have learned that our hypothesis is correct some of the time, but not all of the time- only under certain conditions, even if we yet do not know what those special conditions are.

And that is the point- our understanding is always limited. There is always the possibility that one more test may result in our hypothesis being proved incorrect. This is the fundamental logic of the natural world, and there is no way we can get around it.

But... going back to our hypothesis... now that we know it is correct some of the time and false other times... don't you think we are going to try and chase down under what conditions it is correct and under what conditions it is false. Hmmm. That will require a refined hypothesis. And that my friends is the method by which our science progresses.

Models

When many observations that we do not quite understand are put together, predicting outcomes gets more complicated. In these cases, we create a "model". This can be mathematical or just a visual tool. Models usually describe most of the observed behavior, but may not be siophisticated enough to describe all if it. A model has a limited comprehensiveness; it is only a tool to help visualize a limited number of phenomona. It is useful to the extent that it aids in our understanding and may be a jumping off point from which to build a comprehensive theory.

Theories

Theories are usually mathematical. Theories are based upon several well founded physical princples and are applied to a large range of physical phenomona. For example, whereas a model may describe a single phenomon about a single star, i.e., the cycle of sunspots on the sun, comprehensive theory of stars should incorporate the principles of gravity, conservation of energy, nuclear physics, and hydrostatic equilibrium and describe and predict a larger number of phenomona about stars (i.e., their luminosities, lifetimes, yield of chemical elements, rotation speeds, magentic field strengths, etc).

Natural Laws

Certain physical principles have been tested so many times and have never found to be false so that they are elevated to the stature of Natural Laws. As described above for hypothesis, natural laws can never been proved correct- it is just that we have developed so much faith in them that we believe they will probably never be proved incorrect. An example of a natrual law is the Law of Gravity. Further examples are Newton's Three Laws of Motion, which form the basis for his Theory of Mechanics. Further examples are Kepler's three Laws of Planetary Motion, which it turns out are predicted by Newton's Theory of Mechanics (note: some laws are used to build theory, other laws are deduced via a theory). Last but not least are Kirchoff's Laws of Radiation.

The Babcock Model of the Sunspot Cycle

The best working model of the sunspot cycle is called the Babcock Model. It is only a model because it only tries to deal with a limited number of observations about a limited set of phenomena (that is the behavior of sunspots). The Babcock model is a picture in which the time evolution of the sun's magnetic field is such that it winds up with time due to the sun's differential rotation. The Babcock model provides a reasonable physical scenario that can explain all the data except for one: it cannot predict why the sunspot cycle is 11 years long.