Sunspot Cycle

The number of sunspots reaches a maximum about every 11 years, but successive maxima have spots with reversed magnetic polarity. Thus the whole cycle is 22 years long.

The record of observations indicates that this cycle has been going on back to the early 1700's, although the strength of the cycle varies. For the period 1645 to 1715 the record is rather spotty, but suggests that there were hardly any sunspots.

The luminosity of the Sun increases a little when there are sunspots. During the period 1645 to 1715 the Earth was unusually cold. (The original source for this data is the 1998 SolPhys article by Hoyt and Schatten, "A new construction of Sunspot Numbers." My thanks to Oran White for this information.)

There is a model for how this works. The model makes use of the observation that the upper layers of the Sun rotate faster near the Sun's equator than near its poles. The idea is that the magnetic field gets concentrated along long lines underneath the photosphere and that these likes get stretched out by the differential rotation.

If the field comes out of the photosphere, that makes a pair of sunspots.

An analysis of this model in its details is enormously difficult. But we can ask a few critical questions:

• Does the differential rotation provide the right timescale?
  • At 30 degrees north or south of the equator, it takes 27.5 days for the photosphere to rotate once. Thus this part of the photosphere rotates 365/27.5 = 13.3 times around in a year.
  • At the equator, it takes 25.0 days for the photosphere to rotate once. Thus this part of the photosphere rotates 365/25.0 = 14.6 times around in a year.
  • Thus the equator moves 14.6 - 13.3 = 1.3 times around relative the the area at 30 degrees.
  • That's roughly one wrapping per year, enough to cause quite a tangle in the 5.5 years from a sunspot minimum to a sunspot maximum.
• There is a simple prediction: sunspot pairs should be oriented east-west on the Sun's surface.
• There is another simple prediction:
  • At any one time, in the Sun's northern hemisphere, the eastern spots in sunspot pairs should always have the same magnetic polarity (call it N).
  • The polarity for sunspot pairs in the Sun's southern hemisphere should be the opposite (in this case S).