Seeds of Life in Space (SOLIS). III. Zooming into the methanol peak of the pre-stellar core L1544

Towards the pre-stellar core L1544, the methanol (CH$_3$OH) emission forms an asymmetric ring around the core centre, where CH$_3$OH is mostly in solid form, with a clear peak 4000~au to the north-east of the dust continuum peak. As part of the NOEMA Large Project SOLIS (Seeds of Life in Space), the CH$_3$OH peak has been spatially resolved to study its kinematics and physical structure and to investigate the cause behind the local enhancement. We find that methanol emission is distributed in a ridge parallel to the main axis of the dense core. The centroid velocity increases by about 0.2~km~s$^-1$ and the velocity dispersion increases from subsonic to transonic towards the central zone of the core, where the velocity field also shows complex structure. This could be indication of gentle accretion of material onto the core or interaction of two filaments, producing a slow shock. We measure the rotational temperature and show that methanol is in local thermodynamic equilibrium (LTE) only close to the dust peak, where it is significantly depleted. The CH$_3$OH column density, $N_tot(\rm CH_3OH)$, profile has been derived with non-LTE radiative transfer modelling and compared with chemical models of a static core. The measured $N_tot(\rm CH_3OH)$ profile is consistent with model predictions, but the total column densities are one order of magnitude lower than those predicted by models, suggesting that the efficiency of reactive desorption or atomic hydrogen tunnelling adopted in the model may be overestimated; or that an evolutionary model is needed to better reproduce methanol abundance.