Context : Pure gas-phase chemistry models do not succeed in reproducing the measured abundances of small hydrocarbons in the interstellar medium .
Information on key gas-phase progenitors of these molecules sheds light on this problem .

Aims : We aim to constrain the chemical content of the Horsehead mane with a millimeter unbiased line survey at two positions , namely the photo-dissociation region ( PDR ) and the nearby shielded core .
This project revealed a consistent set of eight unidentified lines toward the PDR position .
We associate them to the l- \mathrm { C _ { 3 } H ^ { + } } hydrocarbon cation , which enables us to constrain the chemistry of small hydrocarbons .
We observed the lowest detectable J line in the millimeter domain along a cut toward the illuminating direction to constrain the spatial distribution of the l- \mathrm { C _ { 3 } H ^ { + } } emission perpendicular to the photo-dissociation front .

Methods : We simultaneously fit 1 ) the rotational and centrifugal distortion constants of a linear rotor , and 2 ) the Gaussian line shapes located at the eight predicted frequencies .
A rotational diagram is then used to infer the excitation temperature and the column density .
We finally compare the abundance to the results of the Meudon PDR photochemical model .

Results : Six out of the eight unidentified lines observable in the millimeter bands are detected with a signal-to-noise ratio from 6 to 19 toward the Horsehead PDR , while the two last ones are tentatively detected .
Mostly noise appears at the same frequency toward the dense core , located less than 40 ^ { \prime \prime } away .
Moreover , the spatial distribution of the species integrated emission has a shape similar to radical species such as HCO , and small hydrocarbons such as \mathrm { C _ { 2 } H } , which show enhanced abundances toward the PDR .
The observed lines can be accurately fitted with a linear rotor model , implying a ^ { 1 } \Sigma ground electronic state .
The deduced rotational constant value is B = 11244.9512 \pm 0.0015 \mathrm { MHz } , close to that of l- \mathrm { C _ { 3 } H } .

Conclusions : This is the first detection of the l- \mathrm { C _ { 3 } H ^ { + } } hydrocarbon in the interstellar medium .
Laboratory spectroscopy is underway to confirm these results .
Interferometric imaging is needed to firmly constrain the small hydrocarbon chemistry in the Horsehead .