The infrared signatures of polycyclic aromatic hydrocarbons (PAHs) are observed in a variety of astrophysical objects, including the circumnuclear medium of active galactic nuclei (AGNs). These are sources of highly energetic photons (0.2 to 10 keV), exposing the PAHs to a harsh environment. In this work, we examined experimentally the photoionization and photostability of naphthalene (C$_{10}$H$_{8}$), anthracene (C$_{14}$H$_{10}$), 2-methyl-anthracene (C$_{14}$H$_{9}$CH$_{3}$) and pyrene (C$_{16}$H$_{10}$) upon interaction with photons of 275, 310 and 2500 eV. The measurements were performed at the Brazilian Synchrotron Light Laboratory using time-of-flight mass-spectrometry (TOF-MS). We determined the absolute photoionization and photodissociation cross sections as a function of the incident photon energy; the production rates of singly, doubly and triply charged ions; and the molecular half-lives in regions surrounding AGNs. Even considering moderate X-ray optical depth values ($tau = 4.45$) due to attenuation by the dusty torus, the half-lives are not long enough to account for PAH detection. Our results suggest that a more sophisticated interplay between PAHs and dust grains should be present in order to circumvent molecular destruction. We could not see any significant difference in the half-life values by increasing the size of the PAH carbon backbone, N$_C$, from 10 to 16. However, we show that the multiple photoionization rates are significantly greater than the single ones, irrespective of the AGN source. We suggest that an enrichment of multiply charged ions caused by X-rays can occur in AGNs.
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