We examine the annihilation of positrons on polycyclic aromatic hydrocarbon (PAH) molecules in interstellar medium conditions. We estimate the annihilation rates of positrons on PAHs by a semi-empirical approach. We show that PAHs can play a significant role in the overall galactic positron annihilation picture and use the annihilation rates and INTEGRAL galactic emission measurements to constrain the amount of PAHs present in the ISM. We find an upper limit of 4.6 x 10^-7 for the PAH abundance.
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