On the origin of C$_4$H and CH$_3$OH in protostellar envelopes

Abstract: 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.