Context : Methanol has a rich rotational spectrum providing a large number of transitions at sub-millimetre wavelengths from a range of energy levels in one single telescope setting , thus making it a good tracer of physical conditions in star-forming regions .
Furthermore , it is formed exclusively on grain surfaces and is therefore a clean tracer of surface chemistry .

Aims : Determining the physical and chemical structure of low-mass , young stellar objects , in particular the abundance structure of CH _ { 3 } OH , to investigate where and how CH _ { 3 } OH forms and how it is eventually released back to the gas phase .

Methods : Observations of the Serpens Molecular Core have been performed at the James Clerk Maxwell Telescope using the array receiver , Harp-B .
Maps over a 4 \aas@@fstack { \prime } 5 \times 5 \aas@@fstack { \prime } 4 region were made in a frequency window around 338 GHz , covering the 7 _ { K } –6 _ { K } transitions of methanol .
Data are compared with physical models of each source based on existing sub-millimetre continuum data .

Results : Methanol emission is extended over each source , following the column density of H _ { 2 } but showing up also particularly strongly around outflows .
The rotational temperature is low , 15–20 K , and does not vary with position within each source .
None of the Serpens Class 0 sources show the high- K lines seen in several other Class 0 sources .
The abundance is typically 10 ^ { -9 } – 10 ^ { -8 } with respect to H _ { 2 } in the outer envelope , whereas “ jumps ” by factors of up to 10 ^ { 2 } –10 ^ { 3 } inside the region where the dust temperature exceeds 100 K are not excluded .
A factor of up to \sim 10 ^ { 3 } enhancement is seen in outflow gas , consistent with previous studies .
In one object , SMM4 , the ice abundance has been measured to be \sim 3 \times 10 ^ { -5 } with respect to H _ { 2 } in the outer envelope , i.e. , a factor of 10 ^ { 3 } larger than the gas-phase abundance .
Comparison with C ^ { 18 } O J =3–2 emission shows that strong CO depletion leads to a high gas-phase abundance of CH _ { 3 } OH not just for the Serpens sources , but also for a larger sample of deeply embedded protostars .

Conclusions : The observations illustrate the large-scale , low-level desorption of CH _ { 3 } OH from dust grains , extending out to and beyond 7500 AU from each source , a scenario which is consistent with non-thermal ( photo- ) desorption from the ice .
The observations also illustrate the usefulness of CH _ { 3 } OH as a tracer of energetic input in the form of outflows , where methanol is sputtered from the grain surfaces .
Finally , the observations provide further evidence of CH _ { 3 } OH formation through CO hydrogenation proceeding on grain surfaces in low-mass envelopes .