On the number and lifetime of 6.7-GHz methanol masers

A statistical estimate of the number of 6.7-GHz methanol masers in the Milky Way and their lifetime is presented. The estimate is based on the currently known number of masers, a realistic correction for sensitivity effects and generally accepted Galactic star formation rates and initial mass functions. The analysis suggests that the minimum number of masers in the Galaxy is of the order of 850 while a more realistic estimate of the total number of masers is of the order of 1200 +/- 84. The lifetime is estimated to be between 2.5 x 10(4) and 4.5 x 10(4) yr, with the variation being due to the use of different initial mass functions. The estimated lifetime agrees with that found from independent studies and agrees remarkably well with the time-scale for the chemical evolution of methanol in hot cores as well as with the dynamical time-scales of molecular outflows associated with high-mass star formation regions. It is shown that the hypothesis of the masers being associated with propagating planar shocks in cores or clumps results in lifetimes for the masers that are smaller by a factor of 2 or more compared with the lifetime of methanol masers as estimated here.