More sulphur in TMC-1: Discovery of the NC${}_3$S and HC${}_3$S radicals with the QUIJOTE line survey

We present the detection of the free radicals NC${}_3$S and HC${}_3$S towards TMC-1 with the QUIJOTE line survey. The derived column densities are (1.4$\pm$0.2)$\times$10${}^{11}$ for NC${}_3$S and (1.5$\pm$0.2)$\times$10${}^{11}$ for HC${}_3$S. We searched for NCCS, but only three transitions are within the domain of our QUIJOTE line survey and the observed lines are marginally detected at the 3$\sigma$ level, providing an upper limit to its column density of $\le$6$\times$10${}^{10}$ cm${}^{-2}$. We also unsuccessfully searched for longer species of the NC${}_n$S (n$\ge$4) and HC${}_n$S (n$\ge$5) families in our TMC-1 data. A chemical model based on a reduced set of reactions involving HC${}_3$S and NC${}_3$S predicts abundances that are 10-100 times below the observed values. These calculations indicate that the most efficient reactions of formation of HC${}_3$S and NC${}_3$S in the model are S + C${}_3$H${}_2$ and N + HC${}_3$S, respectively, while both radicals are very efficiently destroyed through reactions with neutral atoms.