VISIBILITY OF SUNSPOTS

The premier record of long-term solar activity is the sunspot count. This paper will develop a theoretical model of sunspot visibility, collect many large sets on sunspot visibility, test the model against the observations, and develop recommendations for improvements in the calculation of the sunspot count. The theoretical model uses thresholds of visibility from physiological studies, equation governing the effects of telescope optics, and the average properties of sunspots. The result is a predicted threshold size for sunspot visibility with the unaided (but filtered) eye, direct vision through a telescope, pinhole camera, and telescope projection. This paper also reports on over 3250 days of sunspot observations from six observers, 38 yr of daily observations by an experienced observer, 1837 days of observations from a network with over 50 experienced observers, observations from 30 inexperienced observers, as well as summaries of results from 102 AAVSO solar observers. The comparison of the observed thresholds with the predicted thresholds reveals agreement to within the uncertainties, so that the model is validated by observation. To improve the stability of the K factor, it is recommended that only small telescopes (or aperture less than roughly 5 cm) be used, and only at high magnification. For telescope observations, the K-correction factor is accurately given by 14.0/(10 + rho), where rho is the average number of spots in a group as reported by the observer. This formulation for the K factor is not susceptible to long-term drifts and is accurate to roughly 12%.