The detection of complex organic molecules (COMs) toward cold sources such as pre-stellar cores (with T<10 K), has challenged our understanding of the formation processes of COMs in the interstellar medium. Recent modelling on COM chemistry at low temperatures has provided new insight into these processes predicting that COM formation depends strongly on parameters such as visual extinction and the level of CO freeze out. We report deep observations of COMs toward two positions in the L1544 pre-stellar core: the dense, highly-extinguished continuum peak with Av>=30 mag within the inner 2700 au; and a low-density shell with average Av~7.5-8 mag located at 4000 au from the cores center and bright in CH3OH. Our observations show that CH3O, CH3OCH3 and CH3CHO are more abundant (by factors ~2-10) toward the low-density shell than toward the continuum peak. Other COMs such as CH3OCHO, c-C3H2O, HCCCHO, CH2CHCN and HCCNC show slight enhancements (by factors <=3) but the associated uncertainties are large. This suggests that COMs are actively formed and already present in the low-density shells of pre-stellar cores. The modelling of the chemistry of O-bearing COMs in L1544 indicates that these species are enhanced in this shell because i) CO starts freezing out onto dust grains driving an active surface chemistry; ii) the visual extinction is sufficiently high to prevent the UV photo-dissociation of COMs by the external interstellar radiation field; and iii) the density is still moderate to prevent severe depletion of COMs onto grains.
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