Discovery of the interstellar cyanoacetylene radical cation HC$_3$N$^+$

We report the first identification in space of HC$_3$N$^+$, the simplest member of the family of cyanopolyyne cations. Three rotational transitions with half-integer quantum numbers from $J$=7/2 to 11/2 have been observed with the Yebes 40m radio telescope and assigned to HC$_3$N$^+$, which has an inverted $^2\Pi$ ground electronic state. The three rotational transitions exhibit several hyperfine components due to the magnetic and nuclear quadrupole coupling effects of the H and N nuclei. We confidently assign the characteristic rotational spectrum pattern to HC$_3$N$^+$ based on the good agreement between the astronomical and theoretical spectroscopic parameters. We derived a column density of (6.0$\pm$0.6)$\times$10$^{10}$ cm$^{-2}$ and a rotational temperature of 4.5$\pm$1\,K. The abundance ratio between HC$_3$N and HC$_3$N$^+$ is 3200$\pm$320. As found for the larger members of the family of cyanopolyyne cations (HC$_5$N$^+$ and HC$_7$N$^+$), HC$_3$N$^+$ is mainly formed through the reactions of H$_2$ and the cation C$_3$N$^+$ and by the reactions of H$^+$ with HC$_3$N. In the same manner than other cyanopolyyne cations, HC$_3$N$^+$ is mostly destroyed through a reaction with H$_2$ and a dissociative recombination with electrons.