Wolf number

Wolf number since 1750.

The Wolf number (also known as the International sunspot number, relative sunspot number, or Zürich number) is a quantity that measures the number of sunspots and groups of sunspots present on the surface of the sun.

History

The idea of computing sunspot numbers was originated by Rudolf Wolf in 1848^[1] in Zurich, Switzerland and, thus, the procedure he initiated bears his name (or place). The combination of sunspots and their grouping is used because it compensates for variations in observing small sunspots.

This number has been collected and tabulated by researchers for over 150 years.^[2] They have found that sunspot activity is cyclical and reaches its maximum around every 9.5 to 11 years. This cycle was first noted by Heinrich Schwabe in 1843.

Due to weather and researcher unavailability, "the" sunspot count is actually an average of observations by multiple people in multiple locations with different equipment, with a scaling factor k assigned to each observer to compensate for their differing ability to resolve small sunspots and their subjective division of groups of sunspots.^[3]

The relative sunspot number $R$ is computed using the formula (collected as a daily index of sunspot activity):

$R = k(10g + s) \,$

where

• $s$ is the number of individual spots,
• $g$ is the number of sunspot groups, and
• $k$ is a factor that varies with location and instrumentation (also known as the observatory factor or the personal reduction coefficient $K$).^[4]

Revision

Since 1 July 2015 a revised and updated list of the sunspot numbers has been made available.^[3][5] The biggest difference is an overall increase by a factor of 1.6 to the entire series. Traditionally, a scaling of 0.6 was applied to all sunspot counts after 1893, to compensate for Alfred Wolfer's better equipment, after taking over from Wolf. This scaling has been dropped from the revised series, making modern counts closer to their raw values. Also, counts were reduced slightly after 1947 to compensate for bias introduced by a new counting method adopted that year, in which sunspots are weighted according to their size.^[3]

See also

• Solar variation
• Joy's Law (astronomy)

References

1. "The Sun - History". 2001-11-25. Retrieved 2012-01-08.
2. SIDC, RWC Belgium, World Data Center for the Sunspot Index, Royal Observatory of Belgium, 'year(s)-of-data'.
3. Clette, Frédéric; Svalgaard, Leif; Vaquero, José M.; Cliver, Edward W. "Revisiting the Sunspot Number". Space Science Reviews 186 (1-4): 35–103. doi:10.1007/s11214-014-0074-2. ISSN 0038-6308. On average, the observed sunspot number after 1945 is a factor 1.21 higher than the expected value, again showing the influence of the weighting of sunspots according to size, coinciding with the tenure of Waldmeier
4. personal reduction coefficient K
5. Switching to the new Sunspot Number (1 July 2015)

External links

• The Exploratorium's Guide to Sunspots
• Solar Influences Data Analysis Center (SIDC) for the Sunspot Index
• NASA Solar Physics Sunspot Cycle page and Table of Sunspot Numbers (txt) by month since 1749 CE
• Clement Juglar and the transition from crises theory to business cycle theories