Sunspot Numerology

April 5, 2000 -- Here's a simple math quiz: What do you get if you divide the Dow Jones industrial average by the length of mini-skirts in Paris (in cm)? On April 3, 2000 the answer was 286, nearly the same as the daily sunspot number.

Just another cosmic coincidence? That's right, say scientists. The number of spots on our star has little to do with stock prices or fashion trends. However, like the recent stock market, the number of sunspots is on the rise. Just this week the daily Boulder sunspot number soared to 301, about twice the monthly-averaged value expected when the solar cycle reaches its peak later this year.

Right: The Sun is peppered with spots this week. This white light image of the Sun captured on April 3, 2000, by the Michelson Doppler Imager on the Solar and Heliospheric Observatory (SOHO) shows at least 10 distinct sunspot groups on April 3, 2000. [more images from SOHO]

"These high sunspot counts are not unexpected," says Dr. David Hathaway, a solar physicist at NASA’s Marshall Space Flight Center in Huntsville, Alabama. "On a daily or weekly basis the sunspot number can fluctuate wildly, but when we average the counts over a month they agree fairly well with our predictions."

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Hathaway and his colleagues have been tracking the solar cycle for years, using sophisticated statistical techniques to predict when the sunspot maximum will take place and how big it will be. Their latest results suggest a peak sunspot number of about 140 in mid-2000.

"Sometimes there's confusion among the public -- and even among scientists," says Hathaway, "because the sunspot number curves we predict are for averages over many months. When daily numbers are very large, like 301 on April 2nd, I get lots of email from people asking if [the Solar Maximum] is going to be bigger than we thought. That's certainly possible, but these big daily numbers usually average out over a 30-day period."

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Counting sunspots might seem like simple math, but it's not as straightforward as it sounds. Suppose you looked at the Sun through a pair of (properly filtered) low power binoculars -- you might be able to see two or three large spots. An observer peering through a high-powered telescope might see 10 or 20. A powerful space-based observatory could see even more -- say, 50 to 100. Which is the correct sunspot number?

There are actually two official sunspot numbers in common use. The first, the daily "Boulder Sunspot Number," is computed by the NOAA Space Environment Center using a formula devised by Rudolph Wolf in 1848: R=k (10g+s), where R is the sunspot number; g is the number of sunspot groups on the solar disk; s is the total number of individual spots in all the groups; and k is a variable scaling factor (usually <1) that accounts for observing conditions and the type of telescope (binoculars, space telescopes, etc...). Scientists combine data from lots of observatories -- each with its own k factor -- to arrive at a daily value. The Boulder number is usually about 25% higher than the other official index, the "International Sunspot Number," published daily by the Sunspot Index Data Center in Belgium. Both the Boulder and the International numbers are calculated from the same basic formula, but they incorporate data from different observatories.

Right: Rudolf Wolf devised the basic formula for calculating sunspots in 1848. Today, Wolf sunspot counts continue, since no other index of the sun's activity reaches into the past as far and as continuously. An avid astronomical historian and an unrivaled expert on sunspot lore, Wolf confirmed the existence of a cycle in sunspot numbers. He also more accurately determined the cycle's length to be 11.1 years by using early historical records. [more information from the National Geophysical Data Center]

As a rule of thumb, if you divide either of the official sunspot numbers by 15, you'll get the approximate number of individual sunspots visible on the solar disk if you look at the Sun by projecting its image on a paper plate with a small telescope.

Despite the large numbers of sunspots this week, the Sun is still on track for Solar Max to arrive later this year. However, the expectation that scientists can isolate the precise date and time of a solar maximum is a misconception, says Hathaway. In reality there is no single episode. Instead, the solar maximum will last over an extended period of time, perhaps even two years.

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Above: By combining data about geomagnetic activity during the previous solar cycle with sunspot counts for the current cycle, David Hathaway and collaborators are able to predict when the next sunspot maximum will occur. [Click here for details]. According to their results, the sunspot number will peak beginning in mid-2000. The dotted lines above and below the solid curve line indicate the prediction curve's range of error. The vertical bars indicate the full range of daily sunspot numbers that were averaged to obtain monthly data points. Large excursions, like the one on April 2 when the daily Boulder sunspot number reached 301, are not uncommon.

"Even after the sunspot peak is past, we'll have lots of geomagnetic activity like aurora," says Hathaway. "The reason is that late in the solar cycle you can end up with coronal holes
that dip down near the Sun's equator. It has little or nothing to do with sunspots." Coronal holes allow the Sun's high-speed solar wind to escape and buffet Earth's magnetosphere. This can result in power outages, problems with magnetic navigation systems, and dazzling displays of Northern Lights.

Stay tuned to Science.nasa.gov for more updates about solar and geomagnetic activity as the solar cycle nears it peak.

SOHO is a cooperative project between the European Space Agency (ESA) and NASA. The spacecraft was built in Europe for ESA and equipped with instruments by teams of scientists in Europe and the USA.

Editor's note: The opening paragraph of this story whimsically refers to correlations between stock prices, Parisian fashions, and the sunspot number. To date, statisticians have not discovered a relationship between historical trends in these areas. To learn more about sunspots in history, click here.

Web Links

SunspotCycle.com -daily Boulder sunspot numbers and more about sunspots

Sunspot Cycle Predictions -from the Marshall Space Flight Center

SOHO home page -real-time images, screen savers, and more

Thursday's Classroom -- lesson plans and educational activities about sunspots

Sunspot Numerology

The Boulder sunspot number exceeded 300 this week as the sunspot cycle continued its march toward Solar Max.