A general catalogue of 6.7 GHz methanol masers. II. statistical analysis

Context. Methanol masers at 6.7 GHz are recognised markers of high-mass star formation regions. The study of their distribution in the Galaxy gives important insights into the star formation activity of the Milky Way. We present a statistical analysis on the General Catalogue of 6.7 GHz methanol masers in the Galaxy with the aim of extracting global properties of the masers. Aims. We provide constraints on the luminosity function of 6.7 GHz methanol masers and on their total number in the Galaxy. Methods. We model the spatial distribution of the masers in the Milky Way by using their distribution in galactocentric distance which is unambiguous once a rotation curve for the Galaxy is assumed. This is the starting point for determining the luminosity function of the masers. Results. The luminosity function of 6.7 GHz methanol masers is modelled as a power-law with sharp cutoffs and having an index lying between -1.5 and -2. We also predict the number of detections of methanol masers assuming different sensitivity limits in the observations.