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The chemical and physical evolution of starless and pre-stellar cores are of paramount importance to understanding the process of star formation. The Taurus Molecular Cloud cores TMC 1-C and TMC 1-CP share similar initial conditions and provide an excellent opportunity to understand the evolution of the pre-stellar core phase. We investigated the evolutionary stage of starless cores based on observations towards the prototypical dark cores TMC 1-C and TMC 1-CP, mapping them in the CS $3\rightarrow 2$, C$^{34}$S $3\rightarrow 2$, $^{13}$CS $2\rightarrow 1$, DCN $1\rightarrow 0$, DCN $2\rightarrow 1$, DNC $1\rightarrow 0$, DNC $2\rightarrow 1$, DN$^{13}$C $1\rightarrow 0$, DN$^{13}$C $2\rightarrow 1$, N$_2$H$^+$ $1\rightarrow 0$, and N$_2$D$^+$ $1\rightarrow 0$ transitions. We performed a multi-transitional study of CS and its isotopologs, DCN, and DNC lines to characterize the physical and chemical properties of these cores. We studied their chemistry using the state-of-the-art gas-grain chemical code Nautilus and pseudo time-dependent models to determine their evolutionary stage. Observational diagnostics seem to indicate that TMC 1-C is in a later evolutionary stage than TMC 1-CP, with a chemical age $\sim$1 Myr. TMC 1-C shows signs of being an evolved core at the onset of star formation, while TMC 1-CP appears to be in an earlier evolutionary stage due to a more recent formation or, alternatively, a collapse slowed down by a magnetic support., 26 pages, 10 figures

21 pags., 16 figs., 7 tabs., 2 apps., Context. Sulphur is one of the most abundant elements in the Universe. Surprisingly, sulphuretted molecules are not as abundant as expected in the interstellar medium and the identity of the main sulphur reservoir is still an open question. Aims. Our goal is to investigate the H2S chemistry in dark clouds, as this stable molecule is a potential sulphur reservoir. Methods. Using millimeter observations of CS, SO, H2S, and their isotopologues, we determine the physical conditions and H2S abundances along the cores TMC 1-C, TMC 1-CP, and Barnard 1b. The gas-grain model NAUTILUS is used to model the sulphur chemistry and explore the impact of photo-desorption and chemical desorption on the H2S abundance. Results. Our modeling shows that chemical desorption is the main source of gas-phase H2S in dark cores. The measured H2S abundance can only be fitted if we assume that the chemical desorption rate decreases by more than a factor of 10 when nH > 2 × 104. This change in the desorption rate is consistent with the formation of thick H2O and CO ice mantles on grain surfaces. The observed SO and H2S abundances are in good agreement with our predictions adopting an undepleted value of the sulphur abundance. However, the CS abundance is overestimated by a factor of 5-10. Along the three cores, atomic S is predicted to be the main sulphur reservoir. Conclusions. The gaseous H2S abundance is well reproduced, assuming undepleted sulphur abundance and chemical desorption as the main source of H2S. The behavior of the observed H2S abundance suggests a changing desorption efficiency, which would probe the snowline in these cold cores. Our model, however, highly overestimates the observed gas-phase CS abundance. Given the uncertainty in the sulphur chemistry, we can only conclude that our data are consistent with a cosmic elemental S abundance with an uncertainty of a factor of 10., We thank the Spanish MINECO for funding support from AYA2016-75066-C2-1/2-P, AYA2017-85111P, and ERC under ERC-2013-SyG, G. A. 610256 NANOCOSMOS. JM acknowledges the support of ERC-2015-STG No. 679852 RADFEEDBACK. S.P.T.M. acknowledge to the European Union’s Horizon 2020 research and innovation program for funding support given under grant agreement No 639459 (PROMISE).