tokens: Vidal et al. (2017) calculate a CS/HCS + ratio in better agreement with observations, especially at late times. The reason for the low abundance of HCS + in our gas-phase model may be related to the underproduction of H 2 S (see e.g. Agúndez Wakelam 2013 ), which is enhanced when including grain-surface chemistry, and which can increase the abundance of HCS + through reactions like H 2 S + C + and H 2 S + + C. While the calculated abundance of HC 2 S + is in agreement with the observed upper limit, the calculated C 2 S/HC 2 S + ratio is too low because the chemical model severely underestimates the abundance of C 2 S. This is because the chemical network kida.uva.2014 includes an efficient destruction channel for C 2 S through reaction with O atoms, based on estimations by Loison et al. (2012) . If this reaction is neglected, the calculated abundance of C 2 S is shifted up and becomes very close to the observed value, while the abundance of HC 2 S + also increases, remaining consistent with the observed upper limit (see dotted lines in Fig. 3 ). Accurate calculations of the rate constant of the O + C 2 S reaction at low temperatures are needed to shed light on the chemistry of C 2 S in cold dense clouds. 7. Conclusions We report the first identification in space of protonated C 3 S. Four harmonically related lines observed toward TMC-1 using the Yebes 40 m radiotelescope have been unambiguously assigned to this ion thanks to accurate ab initio quantum chemical calculations and laboratory measurements of the rotational spectrum of this species. The derived C 3 S/HC 3 S + ratio of 55 ± 20 is well reproduced by a gas-phase chemical model in which HC 3 S + is mostly formed through protonation of C 3 S and the reactions S + + C 3 H 2 and S + C 3 . Appendix A: Column densities under LTE for linear molecules The determination of column densities from the observed line paramaters of the rotational transitions of a molecule requires knowledge of the collisional rates of the molecular species under study. These values are not always available and rotational diagrams are used to derived rotational temperatures, T r , and column densities ( Goldsmith Langer 1999 ). Often only one line has been observed and therefore an assumption has to be made as to the rotational temperature. The line parameters of the species studied in this paper are given in Table A.1 . Table A.1. Observed line parameters in TMC-1 for CS, HCS + , C 2 S and C 3 S. Notes. (a) Predicted frequencies from the MADEX code ( Cernicharo et al. 2012 ). Numbers in parentheses are 1 σ uncertainties in units of the last digits. (b) Integrated line intensity in K km s −1 . (c) Line velocity with respect to the Local Standard of Rest in km s −1 . (d) Linewidth at half intensity derived by fitting a Gaussian function to the observed line profile (in km s −1 ). (e) Antenna temperature in K. In this section we analyse how the derived column density depends on the adopted T r for a range of
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