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

The Maunder minimum (MM) of greatly reduced solar activity took place in 1645-1715, but the exact level of sunspot activity is uncertain as based, to a large extent, on historical generic statements of the absence of spots on the Sun. Here we aim, using a conservative approach, to assess the level and length of solar cycle during the Maunder minimum, on the basis of direct historical records by astronomers of that time. A database of the active and inactive days (days with and without recorded sunspots on the solar disc respectively) is constructed for three models of different levels of conservatism (loose ML, optimum MO and strict MS models) regarding generic no-spot records. We have used the active day fraction to estimate the group sunspot number during the MM. A clear cyclic variability is found throughout the MM with peaks at around 1655--1657, 1675, 1684 and 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 very low in accordance with a grand minimum of solar activity. We have found, for the core MM (1650-1700), that: (1) A large fraction of no-spot records, corresponding 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 $9\pm 1$ years, but there is an uncertainty in that. (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.