FREQUENCY OF MAUNDER MINIMUM EVENTS IN SOLAR-TYPE STARS INFERRED FROM ACTIVITY AND METALLICITY OBSERVATIONS

We consider the common proposition that the fraction of chromospherically very inactive stars in a solar-type sample is analogous to the fraction of the Sun's main-sequence lifetime spent in a grand minimum state. In a new approach to this proposition, we examine chromospheric activity log R'(HK) in a stellar sample having Hipparcos parallax measurements, and having spectroscopically determined metallicity close to solar (-0.1 <= [Fe/H] <= 0.1). We evaluate height above the Hipparcos main sequence, and estimate age using isochrones, to identify the most Sun-like stars in this sample. As a threshold below which a star is labeled very inactive, we use the peak of the HK activity distribution mapped over the quiet Sun during the 1968 epoch. We estimate the fraction of Maunder Minimum (MM) analog candidates in our sample at 11.1%. Given the 70 yr duration of the historical MM, this suggests that in any given year there is a 1/630 chance of entering a similar grand minimum. There are three important cautions with this type of estimate. First, recent investigation using actual activity and photometric time series has suggested that very low activity may not be a necessary criterion for identifying a non-cycling MM analog candidate. Second, this type of estimate depends very strongly on the choice of very low activity threshold. Third, in instantaneous measurements of log R'(HK), it is not always clear whether a star is a viable MM analog candidate or merely an older star nearing the end of its main-sequence lifetime.