On the origin of C$_4$H and CH$_3$OH in protostellar envelopes
  The formation pathways of different types of organic molecules in
protostellar envelopes and other regions of star formation are subjects of
intense current interest. We here present observations of C$_4$H and CH$_3$OH,
tracing two distinct groups of interstellar organic molecules, toward 16
protostars in the Ophiuchus and Corona Australis molecular clouds. Together
with observations in the literature, we present C$_4$H and CH$_3$OH data from
single-dish observations of 40 embedded protostars. We find no correlation
between the C$_4$H and CH$_3$OH column densities in this large sample. Based on
this lack of correlation, a difference in line profiles between C$_4$H and
CH$_3$OH, and previous interferometric observations of similar sources, we
propose that the emission from these two molecules is spatially separated, with
the CH$_3$OH tracing gas that has been transiently heated to high ($\sim$70-100
K) temperatures, and the C$_4$H tracing the cooler large-scale envelope where
CH$_4$ molecules have been liberated from ices. These results provide insight
in the differentiation between hot corino and warm carbon-chain chemistry in
embedded protostars.
