Decreasing Sunspot Magnetic Fields Explain Unique 10.7 cm Radio Flux

Infrared spectral observations of sunspots from 1998-2011 have shown that on average sunspots changed; the magnetic fields weakened and the temperatures rose. The data also show that sunspots or dark pores can only form at the solar surface only if the magnetic field strength exceeds about 1500 Gauss. Sunspots appear at the solar surface with a variety of field strengths, and during the period from 1998-2002 a histogram of the sunspot magnetic fields shows a normal distribution with a mean of 2436 ±26 Gauss and a width of 323 ±20 Gauss. During this observing period the mean of the magnetic field distribution decreased by 46 ±6 Gauss per year, and we assume that as the 1500 Gauss threshold was approached, magnetic fields appeared at the solar surface which could not form dark sunspots or pores. With this assumption we propose a quantity called the sunspot formation fraction and give an analytical form derived from the magnetic field distribution. We show this fraction can quantitatively explain the changing relationship between sunspot number and solar radio flux measured at 10.7cm wavelengths. Subject headings: Sun: sunspots, Sun: infrared