Context. Hot corinos are extremely rich in complex organic molecules (COMs). Accurate abundance measurements of COMs in such objects are crucial to constrain astrochemical models. In the particular case of close binary systems this can only be achieved through high angular resolution imaging. Aims. We aim to perform an interferometric study of multiple COMs in NGC 1333 IRAS 4A, which is a protostellar binary hosting hot corino activity, at an angular resolution that is sufficient to distinguish easily the emission from the two cores separated by 1.8″. Methods. We used the Atacama Large (sub-)Millimeter Array (ALMA) in its 1.2 mm band and the IRAM Plateau de Bure Interferometer (PdBI) at 2.7 mm to image, with an angular resolution of 0.5″ (120 au) and 1″ (235 au), respectively, the emission from 11 different organic molecules in IRAS 4A. This allowed us to clearly disentangle A1 and A2, the two protostellar cores. For the first time, we were able to derive the column densities and fractional abundances simultaneously for the two objects, allowing us to analyse the chemical differences between them. Results. Molecular emission from organic molecules is concentrated exclusively in A2, while A1 appears completely devoid of COMs or even simpler organic molecules, such as HNCO, even though A1 is the strongest continuum emitter. The protostellar core A2 displays typical hot corino abundances and its deconvolved size is 70 au. In contrast, the upper limits we placed on COM abundances for A1 are extremely low, lying about one order of magnitude below prestellar values. The difference in the amount of COMs present in A1 and A2 ranges between one and two orders of magnitude. Our results suggest that the optical depth of dust emission at these wavelengths is unlikely to be sufficiently high to completely hide a hot corino in A1 similar in size to that in A2. Thus, the significant contrast in molecular richness found between the two sources is most probably real. We estimate that the size of a hypothetical hot corino in A1 should be less than 12 au. Conclusions. Our results favour a scenario in which the protostar in A2 is either more massive and/or subject to a higher accretion rate than A1, as a result of inhomogeneous fragmentation of the parental molecular clump. This naturally explains the smaller current envelope mass in A2 with respect to A1 along with its molecular richness. The extremely low abundances of organic molecules in A1 with respect to those in A2 demonstrate that the dense inner regions of a young protostellar core lacking hot corino activity may be poorer in COMs than the outer protostellar envelope.
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