On the methanol emission detection in the TW Hya disc: the role of grain
  surface chemistry and non-LTE excitation
  The recent detection of gas-phase methanol (CH$_3$OH) lines in the disc of TW
Hya by Walsh et al. provided the first observational constraints on the complex
O-bearing organic content in protoplanetary discs. The emission has a ring-like
morphology, with a peak at $\sim 30-50$ au and an inferred column density of
$\sim 3-6\times10^{12}$ cm$^{-2}$. A low CH$_3$OH fractional abundance of $\sim
0.3-4\times 10^{-11}$ (with respect to H$_2$) is derived, depending on the
assumed vertical location of the CH$_3$OH molecular layer. In this study, we
use a thermo-chemical model of the TW Hya disc, coupled with the ALCHEMIC
gas-grain chemical model, assuming laboratory-motivated, fast diffusivities of
the surface molecules to interpret the CH$_3$OH detection. Based on this disc
model, we performed radiative transfer calculations with the LIME code and
simulations of the observations with the CASA simulator. We found that our
model allows to reproduce the observations well. The CH$_3$OH emission in our
model appears as a ring with radius of $\sim60$ au. Synthetic and observed line
flux densities are equal within the rms noise level of observations. The
synthetic CH$_3$OH spectra calculated assuming local thermodynamic equilibrium
(LTE) can differ by up to a factor of 3.5 from the non-LTE spectra. For the
strongest lines, the differences between LTE and non-LTE flux densities are
very small and practically negligible. Variations in the diffusivity of the
surface molecules can lead to variations of the CH$_3$OH abundance and,
therefore, line flux densities by an order of magnitude.
