Observed transitions of HC₅N⁺ (left column) and HC₇N⁺ (right column) in TMC-1. Quantum numbers are indicated at the top right of each panel. The abscissa corresponds to the rest frequency. The ordinate is the antenna temperature, corrected for atmospheric and telescope losses, in milli Kelvin. Blanked channels correspond to negative features produced when folding the frequency-switched data. The red line shows the computed synthetic spectra for the lines of the two species (see Sects. 3.1 and 3.2). The physical parameters used for the models are given in Sect. 3.3. The centroids of the modelled lines of HC₅N⁺ have been fixed to the observed ones (see Table A.1) and the simulated hyperfine components have been added to these centroids. For HC₇N⁺ the line frequencies are given in Table A.2.