According to traditional gas-phase chemical models, O2 should be abundant in molecular clouds, but until recently, attempts to detect interstellar O2 line emission with ground- and space-based observatories have failed. Following the multi-line detections of O2 with low abundances in the Orion and rho Oph A molecular clouds with Herschel, it is important to investigate other environments, and we here quantify the O2 abundance near a solar-mass protostar. Observations of O2, at 487 GHz toward a deeply embedded low-mass Class 0 protostar, NGC 1333-IRAS 4A, are presented, using the HIFI instrument on the Herschel Space Observatory. Complementary data of the chemically related NO and CO molecules are obtained as well. The high spectral resolution data are analysed using radiative transfer models to infer column densities and abundances, and are tested directly against full gas-grain chemical models. The deep HIFI spectrum fails to show O2 at the velocity of the dense protostellar envelope, implying one of the lowest abundance upper limits of O2/H2 at <6x10^-9 (3 sigma). However, a tentative (4.5 sigma) detection of O2 is seen at the velocity of the surrounding NGC 1333 molecular cloud, shifted by 1 km/s relative to the protostar. For the protostellar envelope, pure gas-phase models and gas-grain chemical models require a long pre-collapse phase (~0.7-1x10^6 years), during which atomic and molecular oxygen are frozen out onto dust grains and fully converted to H2O, to avoid overproduction of O2 in the dense envelope. The same model also reproduces the limits on the chemically related NO molecule. The tentative detection of O2 in the surrounding cloud is consistent with a low-density PDR model with small changes in reaction rates. The low O2 abundance in the collapsing envelope around a low-mass protostar suggests that the gas and ice entering protoplanetary disks is very poor in O2.
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