OBSERVATIONS OF HYSTERESIS IN SOLAR-CYCLE VARIATIONS AMONG M SOLAR-ACTIVITY INDICATORS

We show that smoothed time series of 7 indices of solar activity exhibit significant solar cycle dependent differences in their relative variations during the past 20 years. In some cases these observed hysteresis patterns start to repeat over more than one solar cycle, giving evidence that this is a normal feature of solar variability. Among the indices we study, we find that the hysteresis effects are approximately simple phase shifts, and we quantify these phase shifts in terms of lag times behind the leading index, the International Sunspot Number. Our measured lag times range from less than one month to greater than four months and can be much larger than lag times estimated from short-term variations of these same activity indices during the emergence and decay of major active regions. We argue that hysteresis represents a real delay in the onset and decline of solar activity and is an important clue in the search for physical processes responsible for changing solar emission at various wavelengths.