  Complex organic molecules (COMs) have been detected in a variety of
environments, including cold prestellar cores. Given the low temperature of
these objects, these last detections challenge existing models. We report here
new observations towards the prestellar core L1544. They are based on an
unbiased spectral survey of the 3mm band at the IRAM-30m telescope, as part of
the Large Program ASAI. The observations allow us to provide the full census of
the oxygen bearing COMs in this source. We detected tricarbon monoxide,
methanol, acetaldehyde, formic acid, ketene, and propyne with abundances
varying from 5e-11 to 6e-9. The non-LTE analysis of the methanol lines shows
that they are likely emitted at the border of the core, at a radius of ~8000 AU
where T~10 K and nH2~2e4 cm-3. Previous works have shown that water vapour is
enhanced in the same region because of the photodesorption of water ices. We
propose that a non-thermal desorption mechanism is also responsible for the
observed emission of methanol and COMs from the same layer. The desorbed oxygen
and a tiny amount of desorbed methanol and ethene are enough to reproduce the
abundances of tricarbon monoxide, methanol, acetaldehyde and ketene measured in
L1544. These new findings open the possibility that COMs in prestellar cores
originate in a similar outer layer rather than in the dense inner cores, as
previously assumed, and that their formation is driven by the non-thermally
desorbed species.
