The Evolutionary Status of Protostellar Clumps Hosting Class II Methanol
  Masers
  The Methanol MultiBeam survey (MMB) provides the most complete sample of
Galactic massive young stellar objects (MYSOs) hosting 6.7GHz class II methanol
masers. We characterise the properties of these maser sources using dust
emission detected by the Herschel Infrared Galactic Plane Survey (Hi-GAL) to
assess their evolutionary state. Associating 731 (73%) of MMB sources with
compact emission at four Hi-GAL wavelengths, we derive clump properties and
define the requirements of a MYSO to host a 6.7GHz maser. The median
far-infrared (FIR) mass and luminosity are 630M$_{\odot}$ and 2500L$_{\odot}$
for sources on the near side of Galactic centre and 3200M$_{\odot}$ and
10000L$_{\odot}$ for more distant sources. The median luminosity-to-mass ratio
is similar for both at $\sim$4.2L$_{\odot}/$M$_{\odot}$. We identify an
apparent minimum 70$\mu$m luminosity required to sustain a methanol maser of a
given luminosity (with $L_{70} \propto L_{6.7}^{0.6}$). The maser host clumps
have higher mass and higher FIR luminosities than the general Galactic
population of protostellar MYSOs. Using principal component analysis, we find
896 protostellar clumps satisfy the requirements to host a methanol maser but
lack a detection in the MMB. Finding a 70$\mu$m flux density deficiency in
these objects, we favour the scenario in which these objects are evolved beyond
the age where a luminous 6.7GHz maser can be sustained. Finally, segregation by
association with secondary maser species identifies evolutionary differences
within the population of 6.7GHz sources.
