Top-down formation of fullerenes in the interstellar medium

Abstract

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.

Keywords: ISM: molecules; Methods: numerical; astrochemistry; molecular processes.

Fig. 1

Schematic representation of the evolutionary scenario for the formation of fullerenes from PAHs under UV irradiation.

Fig. 2

Cooling rates for C₆₀ as a function of the internal energy of the molecule. The infrared emission and cooling by fluorescence from thermally excited electronic states are calculated (labelled Poincaré in the figure) following the formalism described in this paper. The thermionic emission rates are taken from Hansen et al. (2003).

Fig. 3

Physical conditions in NGC 7023. Density profile derived from observations of the far-infrared dust emission in the cavity of NGC 7023 (blue with error-bars) and exponential fit to this profile used in the photochemical model (red line). The black line shows the adopted profile for the intensity of the radiation field G₀.

Fig. 4

Probability density function of dissociation of the C₆₀ molecule as a function of internal energy, at a distance of 5” from the star (G₀ ~ 2 × 10⁵). Energies E_peak at maximum dissociation rate (D(E) = k_diss(E) × n(E)), E_low and E_up (where D(E_up) = D(E_low) = D(E_peak)/100 and E_up > E_low) are depicted. The values of E_peak, E_low and E_up for all cages are given in Table 3.

Fig. 5

Model results for the time-evolution of the abundance of PAHs $(\sum _{n=1}^{20}{\mathrm{C}}_{66}{\mathrm{H}}_n)$, and cages $({\mathrm{C}}_{66}^{\mathit{planar}},{\mathrm{C}}_{66}^{\mathit{cage}},{\mathrm{C}}_{64}^{\mathit{cage}},{\mathrm{C}}_{62}^{\mathit{cage}},{\mathrm{C}}_{60}^{\mathit{cage}},{\mathrm{C}}_{58}^{\mathit{cage}})$ and C₂. These are normalized to the abundance of C₆₆H₂₀ at t = 0. The model calculations are done for distances of 5, 10, 15, 20 and 25” from the star HD 200775 in NGC 7023. Note that the dissociation of C₂ is not treated in our model, hence the C₂ abundances reported are only provided as an indication of how much C₂ is formed from the dissociation of cages. Similarly, the dissociation of the ${\mathrm{C}}_{56}^{\mathit{cage}}$ is not included in the model and therefore its abundance is provided as an indication of how much C₆₀ is being destroyed. The gray shadowed regions indicate the uncertainty range implied by uncertainties of a factor of 10 on the rates of C₂ loss (see Sect. 4.3 for details). The approximate age of NGC 7023 is given, with orange shadowed regions representing the uncertainty on this value (see Sect. 3 for details).