Stability of polycyclic aromatic hydrocarbon clusters in protoplanetary discs

Context. The infrared signature of polycyclic aromatic hydrocarbons (PAHs) is present in many protostellar discs, and these species are thought to play an important role in the heating of the gas in the photosphere. Aims. We consider PAH cluster formation as one possible cause for non-detections of PAH features in protoplanetary discs. We test the necessary conditions for cluster formation and cluster dissociation by stellar optical and far-UV photons in protoplanetary discs using a Herbig Ae/Be and a T Tauri star disc model. Methods. We perform Monte Carlo and statistical calculations to determine dissociation rates for coronene, circumcoronene, and circumcoronene clusters with sizes of between 2 and 200 cluster members. By applying general disc models to our Herbig Ae/Be and T Tauri star model, we estimate the formation rate of PAH dimers and compare these with the dissociation rates. Results. We show that the formation of PAH dimers can take place in the inner 100 AU of protoplanetary discs in sub-photospheric layers. Dimer formation takes seconds to years, allowing them to grow beyond dimer size in a short time. We further demonstrate that PAH clusters increase their stability while they grow when they are located beyond a critical distance that depends on stellar properties and PAH species. The comparison with the local vertical mixing timescale allows a determination of the minimum cluster size necessary for the survival of PAH clusters. Conclusions. Considering the PAH cluster formation sites, cluster survival in the photosphere of the inner disc of Herbig stars is unlikely because of the high UV radiation. For the T Tauri stars, survival of coronene, circumcoronene, and circumcircumcoronene clusters is possible, and cluster formation should be considered as one possible explanation for low PAH detection rates in T Tauri star discs