Context: PAHs are thought to be a ubiquitous and important dust component of the interstellar medium. However, the effects of their immersion in a hot (post-shock) gas have never before been fully investigated. Aims: We study the effects of energetic ion and electron collisions on PAHs in the hot post-shock gas behind interstellar shock waves. Methods: We calculate the ion-PAH and electron-PAH nuclear and electronic interactions, above the carbon atom loss threshold, in H II regions and in the hot post-shock gas, for temperatures ranging from 10^3 to 10^8 K. Results: PAH destruction is dominated by He collisions at low temperatures (T < 3x10^4 K), and by electron collisions at higher temperatures. Smaller PAHs are destroyed faster for T < 10^6 K, but the destruction rates are roughly the same for all PAHs at higher temperatures. The PAH lifetime in a tenuous hot gas (n_H ~ 0.01 cm^-3, T ~ 10^7 K), typical of the coronal gas in galactic outflows, is found to be about thousand years, orders of magnitude shorter than the typical lifetime of such objects. Conclusions: In a hot gas, PAHs are principally destroyed by electron collisions and not by the absorption of X-ray photons from the hot gas. The resulting erosion of PAHs occurs via C_2 loss from the periphery of the molecule, thus preserving the aromatic structure. The observation of PAH emission from a million degree, or more, gas is only possible if the emitting PAHs are ablated from dense, entrained clumps that have not yet been exposed to the full effect of the hot gas.
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