A method to measure CO and N

Context. In the dense and cold prestellar cores, many species freeze out onto grains to form ices. The most conspicuous case is that of CO itself. Only upper limits of this depletion amplitude can be estimated because the CO emission from the external undepleted layers mask the emission of CO left inside the depleted region. The finite signal-to-noise ratio of the observations is another limitation. However, depletion and even more desorption mechanisms are not well-known and need observational constraints, i.e., depletion profiles. Aims. We describe a method for retrieving the CO and N2 abundance profiles inside prestellar cores, which is mostly free of initial conditions. Methods. DCO+ is a daughter molecule of CO, which appears inside depleted prestellar cores. The main deuteration partners are the H3+ isotopologues. By determining the abundance of these isotopologues via N2D+, N2H+, and ortho-H2D+ observations and a chemical model, we can uniquely constrain the CO abundance, the only free parameter left, to fit the observed DCO+ abundance. The N2 abundance is also determined in the same manner once CO is known. DCO+–H2 collisional rates including the hyperfine structure were computed in order to determine the DCO+ abundance. Results. To illustrate the method, we apply it to the main L18