Spin-down of cool stars during their main-sequence life

A parametric formula describing the magnetic braking of a star via a thermal wind together with an empirical relation between the stellar Rossby number and the filling factor describing a coverage of the stellar surface with strong magnetic fields is used to derive an analytical formula for variation of the rotation period of a dwarf star with time. The derived formula applies to stars rotating with periods not shorter than about 1 day. Constants appearing in this formula are determined using observations of calcium emission in stellar clusters. The values of the constants obtained in this way are in agreement with data on the present spin-down rate of the sun and the rotation of individual stars of known age. It is demonstrated that the derived formula predicts correctly the distribution of periods of rotation observed among Hyades stars as well as among old stars from the solar neighborhood.