Level and length of cyclic solar activity during the Maunder minimum as deduced from the active-day statistics

Aims. The Maunder minimum (MM) of greatly reduced solar activity took place in 1645-1715, but the exact level of sunspot activity is uncertain because it is based, to a large extent, on historical generic statements of the absence of spots on the Sun. Using a conservative approach, we aim to assess the level and length of solar cycle during the MM on the basis of direct historical records by astronomers of that time. Methods. A database of the active and inactive days (days with and without recorded sunspots on the solar disc) is constructed for three models of different levels of conservatism (loose, optimum, and strict models) regarding generic no-spot records. We used the active day fraction to estimate the group sunspot number during the MM. Results. A clear cyclic variability is found throughout the MM with peaks at around 1655-1657, 1675, 1684, 1705, and possibly 1666, with the active-day fraction not exceeding 0.2, 0.3, or 0.4 during the core MM, for the three models. Estimated sunspot numbers are found to be very low in accordance with a grand minimum of solar activity. Conclusions. For the core MM (1650-1700), we have found that (1) A large portion of no-spot records, which correspond to the solar meridian observations, may be unreliable in the conventional database. (2) The active-day fraction remained low (below 0.3-0.4) throughout the MM, indicating the low level of sunspot activity. (3) The solar cycle appears clearly during the core MM. (4) The length of the solar cycle during the core MM appears for 9 +/- 1 years, but this is uncertain. (5) The magnitude of the sunspot cycle during MM is assessed to be below 5-10 in sunspot numbers. A hypothesis of the high solar cycles during the MM is not confirmed.