Photodissociation in proto-planetary nebulae Hydrodynamical simulations and solutions for low-velocity multi-lobes

Aims. We explore the effects of photodissociation at the stages of post-asymptotic giant branch stars to find a mechanism able to produce multi-polar shapes. Methods. We perform two-dimensional gasdynamical simulations to model the effects of photodissociation in proto-planetary nebulae. Results. We find that post-asymptotic giant branch stars with similar to 7000 K or hotter are able to photodissociate a large amount of the circumstellar gas. We compute several solutions for nebulae with low-velocity multi-lobes. We find that the early expansion of a dissociation front is crucial to understand the number of lobes in proto-planetary nebulae. Conclusions. A dynamical instability appears when cooling is included in the swept-up molecular shell. This instability is similar to the one found in photoionization fronts, and it is associated with the thin-shell Vishniac instability. The dissociation front exacerbates the growth of the thin-shell instability, creating a fast fragmentation in shells expanding into media with power-law density distributions such as r(-2).