On the size of the CO-depletion radius in the IRDC G351.77-0.51
  An estimate of the degree of CO-depletion ($f_D$) provides information on the
physical conditions occurring in the innermost and densest regions of molecular
clouds. A key parameter in these studies is the size of the depletion radius,
i.e. the radius within which the C-bearing species, and in particular CO, are
largely frozen onto dust grains. A strong depletion state (i.e. $f_D>10$, as
assumed in our models) is highly favoured in the innermost regions of dark
clouds, where the temperature is $<20$ K and the number density of molecular
hydrogen exceeds a few $\times$10$^{4}$ cm$^{-3}$. In this work, we estimate
the size of the depleted region by studying the Infrared Dark Cloud (IRDC)
G351.77-0.51. Continuum observations performed with the $Herschel$ $Space$
$Observatory$ and the $LArge$ $APEX$ $BOlometer$ $CAmera$, together with APEX
C$^{18}$O and C$^{17}$O J=2$\rightarrow$1 line observations, allowed us to
recover the large-scale beam- and line-of-sight-averaged depletion map of the
cloud. We built a simple model to investigate the depletion in the inner
regions of the clumps in the filament and the filament itself. The model
suggests that the depletion radius ranges from 0.02 to 0.15 pc, comparable with
the typical filament width (i.e.$\sim$0.1 pc). At these radii, the number
density of H$_2$ reaches values between 0.2 and 5.5$\times$10$^{5}$ cm$^{-3}$.
These results provide information on the approximate spatial scales on which
different chemical processes operate in high-mass star-forming regions and also
suggest caution when using CO for kinematical studies in IRDCs.
