Top-down formation of fullerenes in the interstellar medium

Fullerenes have been recently detected in various circumstellar and interstellar environments, raising the question of their formation pathway. It has been proposed that they can form at the low densities found in the interstellar medium by the photo-chemical processing of large polycyclic aromatic hydrocarbons (PAHs). Following our previous work on the evolution of PAHs in the NGC 7023 reflection nebula, we evaluate, using photochemical modeling, the possibility that the PAH C₆₆H₂₀ (i.e. circumovalene) can lead to the formation of C₆₀ upon irradiation by ultraviolet photons. The chemical pathway involves full dehydrogenation of C₆₆H₂₀, folding into a floppy closed cage and shrinking of the cage by loss of C₂ units until it reaches the symmetric C₆₀ molecule. At 10" from the illuminating star and with realistic molecular parameters, the model predicts that 100% of C₆₆H₂₀ is converted into C₆₀ in ~ 10⁵ years, a timescale comparable to the age of the nebula. Shrinking appears to be the kinetically limiting step of the whole process. Hence, PAHs larger than C₆₆H₂₀ are unlikely to contribute significantly to the formation of C₆₀, while PAHs containing between 60 and 66 C atoms should contribute to the formation of C₆₀ with shorter timescales, and PAHs containing less than 60 C atoms will be destroyed. Assuming a classical size distribution for the PAH precursors, our model predicts absolute abundances of C₆₀ are up to several 10^-4 of the elemental carbon, i.e. less than a percent of the typical interstellar PAH abundance, which is consistent with observational studies. According to our model, once formed, C₆₀ can survive much longer (> 10⁷ years for radiation fields below G₀ = 10⁴) than other fullerenes because of the remarkable stability of the C₆₀ molecule at high internal energies. Hence, a natural consequence is that C₆₀ is more abundant than other fullerenes in highly irradiated environments.