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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.