Importance of source structure on complex organics emission II. Can
  disks explain lack of methanol emission from some low-mass protostars?
  Some protostellar systems show little or no millimetre line emission of
complex organics. This can be interpreted as a low abundance of these
molecules, alternatively they could be present in the system but are not seen
in the gas. The goal is to investigate the latter hypothesis for methanol. We
will attempt to answer the question: Does the presence of a disk and optically
thick dust reduce methanol emission even if methanol is abundant in the ices
and gas? Using the radiative transfer code RADMC-3D, methanol emission lines
from an envelope-only model and an envelope-plus-disk model are calculated and
compared with each other and the observations. Methanol emission from the
envelope-only model is always stronger than from the envelope-plus-disk model
by at least a factor 2 as long as the disk radius is larger than 30 au (for L=8
L$_{\odot}$). In most cases, this is due to lower temperatures and, hence, the
smaller amount of warm methanol inside the snow surface of the
envelope-plus-disk model. The intensities drop by more than an order of
magnitude for models including high mm opacity dust grains and disk radii of at
least 50 au (for L=8 L$_{\odot}$) due to continuum over-subtraction. The line
intensities from the envelope-only models overproduce the observations of
protostars with lower methanol emission even with large dust optical depth
effects. The envelope-plus-disk models can explain the bulk of the
observations. However, they can only reproduce the observations of sources with
high luminosities and low methanol emission when dust optical depth effects
especially continuum over-subtraction in the disk becomes effective. Therefore,
both the effects of disk and dust optical depth should be considered to explain
the observations. In conclusion: Absence of methanol emission does not imply
absence of methanol molecules in either gas or ice.
