Blinded by the light: on the relationship between CO first overtone
  emission and mass accretion rate in massive young stellar objects
  To date, there is no explanation as to why disc-tracing CO first overtone (or
`bandhead') emission is not a ubiquitous feature in low- to medium-resolution
spectra of massive young stellar objects, but instead is only detected toward
approximately 25 per cent of their spectra. In this paper, we investigate the
hypothesis that only certain mass accretion rates result in detectable bandhead
emission in the near infrared spectra of MYSOs. Using an analytic disc model
combined with an LTE model of the CO emission, we find that high accretion
rates ($\gtrsim 10^{-4}\,{\rm M}_{\odot}{\mathrm{yr}}^{-1}$) result in large
dust sublimation radii, a larger contribution to the $K$-band continuum from
hot dust at the dust sublimation radius, and therefore correspondingly lower CO
emission with respect to the continuum. On the other hand, low accretion rates
($\lesssim10^{-6}\,{\rm M}_{\odot}{\mathrm{yr}}^{-1}$) result in smaller dust
sublimation radii, a correspondingly smaller emitting area of CO, and thus also
lower CO emission with respect to the continuum. In general, moderate accretion
rates produce the most prominent, and therefore detectable, CO first overtone
emission. We compare our findings to a recent near-infrared spectroscopic
survey of MYSOs, finding results consistent with our hypothesis. We conclude
that the detection rate of CO bandhead emission in the spectra of MYSOs could
be the result of MYSOs exhibiting a range of mass accretion rates, perhaps due
to the variable accretion suggested by recent multi-epoch observations of these
objects.
