  Small hydrocarbons, such as C2H, C3H and C3H2 are more abundant in
photo-dissociation regions (PDRs) than expected based on gas-phase chemical
models. To explore the hydrocarbon chemistry further, we observed a key
intermediate species, the hydrocarbon ion l-C3H+, in the Horsehead PDR with the
Plateau de Bure Interferometer at high-angular resolution (6''). We compare
with previous observations of C2H and c-C3H2 at similar angular resolution and
new gas-phase chemical model predictions to constrain the dominant formation
mechanisms of small hydrocarbons in low-UV flux PDRs. We find that, at the peak
of the HCO emission (PDR position), the measured l-C3H+, C2H and c-C3H2
abundances are consistent with current gas-phase model predictions. However, in
the first PDR layers, at the 7.7 mum PAH band emission peak, which are more
exposed to the radiation field and where the density is lower, the C2H and
c-C3H2 abundances are underestimated by an order of magnitude. At this
position, the l-C3H+ abundance is also underpredicted by the model but only by
a factor of a few. In addition, contrary to the model predictions, l-C3H+ peaks
further out in the PDR than the other hydrocarbons, C2H and c-C3H2. This cannot
be explained by an excitation effect. Current gas-phase photochemical models
thus cannot explain the observed abundances of hydrocarbons, in particular in
the first PDR layers. Our observations are consistent with a top-down
hydrocarbon chemistry, in which large polyatomic molecules or small
carbonaceous grains are photo-destroyed into smaller hydrocarbon
molecules/precursors.
