The RMS survey: The luminosity functions and timescales of massive young stellar objects and compact H II regions

We present a determination of the luminosity functions of massive young stellar objects (MYSOs) and compact (C) H II regions within the Milky Way using the large, well-selected sample of these sources identified by the Red MSX Source survey. The MYSO luminosity function decreases monotonically such that there are few with Lgsim105 L ?, while the CH II regions are detected up to ~106 L ?. The lifetimes of these phases are also calculated as a function of luminosity by comparison with the luminosity function for local main-sequence OB stars. These indicate that the MYSO phase has a duration ranging from 4×105 yr for 104 L ? to ~7×104 yr at 105 L ?, while the CH II region phase lasts of order 3×105 yr or ~3%-10% of the exciting star's main-sequence lifetime. MYSOs between 104 L ? and ~105 L ? are massive but do not display the radio continuum or near-IR H I recombination line emission indicative of an H II region, consistent with being swollen due to high ongoing or recent accretion rates. Above ~105 L ? the MYSO phase lifetime becomes comparable to the main-sequence Kelvin-Helmholtz timescale, at which point the central star can rapidly contract onto the main sequence even if still accreting, and ionize a CH II region, thus explaining why few highly luminous MYSOs are observed.