ATLASGAL -- physical parameters of dust clumps associated with 6.7 GHz methanol masers

We have constructed the largest sample of dust-associated class II 6.7 GHz methanol masers yet obtained. New measurements from the the Methanol MultiBeam (MMB) Survey were combined with the 870 $\mu$m APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) and the 850 $\mu$m JCMT Plane Survey (JPS). Together with two previous studies we have now identified the host clumps for 958 methanol masers across the Galactic Plane, covering approximately 99% of the MMB catalogue and increasing the known sample of dust-associated masers by over 30%. We investigate correlations between the physical properties of the clumps and masers using distances and luminosities drawn from the literature. Clumps hosting methanol masers are significantly more compact and have higher volume densities than the general population of clumps. We determine a minimum volume density threshold of $n$(H$_2$) $\geq 10^4$ cm$^{-3}$ for the efficient formation of intermediate- and high-mass stars. We find 6.7 GHz methanol masers are associated with a distinct part of the evolutionary process ($L_{\rm bol}$/$M_{\rm fwhm}$ ratios of between 10$^{0.6}$ and 10$^{2.2}$) and have well defined turning on and termination points. We estimate the lower limit for the mass of embedded objects to be $\geq$ 6 M$_{\odot}$ and the statistical lifetime of the methanol maser stage to be $\sim$ 3.3$\times$10$^{4}$ yrs. This suggests that methanol masers are indeed reliable tracers of high mass star formation, and indicates that the evolutionary period traced by this marker is relatively rapid.