We compare the average level of chromospheric activity and cycle length for solar-type stars as determined from 25 yr records of Ca II fluxes and from the sunspot record from 1750 to 1990. Both sets of data show an inverse relation between the cycle length and average activity level, with only a minor difference in the slopes. In turn, the amplitude of Ca II variability is positively correlated with the photometric brightness change during an activity cycle. The relationship between those observables provides a physical basis for the close correlation between the length of the sunspot cycle and mean terrestrial temperature over the last few centuries as shown by Friis-Christensen & Lassen. Solar brightness variations over the last several centuries can be estimated from this relationship by including stars with low Ca II fluxes which, we assume, are in states resembling the phase of solar activity known as the Maunder minimum (circa 1645-1715). Although the value of the slope connecting the mean level of Ca II activity and the cycle length is sensitive to the statistical treatment of the data, a lower limit to the slope can be determined reliably. This lower limit yields an increase of 0.4% of solar brightness from the solar Maunder minimum to the cyclic phase of sunspot activity which immediately followed the Maunder minimum.
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Baliunas et al. (1995) studied this question.