We present maps at high spatial and spectral resolution in emission lines of C2H, c-C3H2, C4H, 12CO and C18O of the edge of the Horsehead nebula obtained with the Plateau de Bure Interferometer (PdBI). The edge of the Horsehead nebula is a one-dimensional Photo--Dissociation Region (PDR) viewed almost edge-on. All hydrocarbons are detected at high signal--to--noise ratio in the PDR where intense emission is seen both in the H2 ro-vibrational lines and in the PAH mid--infrared bands. C18O peaks farther away from the cloud edge. Our observations demonstrate that C2H, cC3H2 and C4H are present in UV--irradiated molecular gas, with abundances nearly as high as in dense, well shielded molecular cores. PDR models i) need a large density gradient at the PDR edge to correctly reproduce the offset between the hydrocarbons and H2 peaks and ii) fail to reproduce the hydrocarbon abundances. We propose that a new formation path of carbon chains, in addition to gas phase chemistry, should be considered in PDRs: because of intense UV--irradiation, large aromatic molecules and small carbon grains may fragment and feed the interstellar medium with small carbon clusters and molecules in significant amount.
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