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Cosmic Rays (CR) process the matter of the Interstellar Medium. Such energetic processing not only modifies the interstellar matter but also injects chemical species in the gas phase. In this work, we study the effect of the CR on the astrophysical polycyclic aromatic hydrocarbons (PAH). For events in which many electrons are stripped out from the PAH by interaction with a heavy cosmic ray particle, coulomb explosion takes place and carbon chains are produced. The fragments production rates of carbon chains are of particular interest for astrophysical models. We computed PAH multi-ionization cross sections with an Independent Atom and Electron collisional model. We introduced and used a model to predict the fragmentation pattern for the coulomb explosion. Experimental measurements on small hydrocarbons, C$_{60}$ and PAHs were used to set confidence intervals on the calculations results.   The carbon chains production rates were calculated using different CR fluxes and elemental compositions, to account for the variations expected in various astrophysical environments. A range of PAH sizes and compactness were also explored. The PAH lifetime with respect to a standard interstellar CR flux (corresponding to an H$_2$ ionization rate of $\zeta \approx$ 6.10$^{-17}$s$^{-1}$) is found to be in the order of a few billion years. The production rates of interstellar carbon chains containing around 5-15 carbon atoms are in the order of few to many tens of percent of the H$_2$ ionization rate $\zeta$. The exact rate value relies on the nature of the PAH and on the CR composition. In diffuse medium, with ten percent of the available cosmic carbon locked in PAHs, this process leads to carbon chain fractional abundances at steady state, in the range of $10^{-15}$-$10^{-14}$, with a confidence interval of about one order of magnitude. It reaches $10^{-13}$ in quiescent dense clouds.

Coulomb Explosion of Polycyclic Aromatic Hydrocarbons Induced by Heavy Cosmic Rays: Carbon Chains Production Rates