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An estimate of the degree of CO-depletion ($f_D$) provides information on thephysical conditions occurring in the innermost and densest regions of molecularclouds. 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, arelargely frozen onto dust grains. A strong depletion state (i.e. $f_D>10$, asassumed in our models) is highly favoured in the innermost regions of darkclouds, where the temperature is $<20$ K and the number density of molecularhydrogen exceeds a few $\times$10$^{4}$ cm$^{-3}$. In this work, we estimatethe 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 APEXC$^{18}$O and C$^{17}$O J=2$\rightarrow$1 line observations, allowed us torecover the large-scale beam- and line-of-sight-averaged depletion map of thecloud. We built a simple model to investigate the depletion in the innerregions of the clumps in the filament and the filament itself. The modelsuggests that the depletion radius ranges from 0.02 to 0.15 pc, comparable withthe typical filament width (i.e.$\sim$0.1 pc). At these radii, the numberdensity of H$_2$ reaches values between 0.2 and 5.5$\times$10$^{5}$ cm$^{-3}$.These results provide information on the approximate spatial scales on whichdifferent chemical processes operate in high-mass star-forming regions and alsosuggest caution when using CO for kinematical studies in IRDCs.

On the size of the CO-depletion radius in the IRDC G351.77-0.51