Can X-rays provide a solution to the abundance discrepancy problem in photoionised nebulae?

We re-examine the well-known discrepancy between ionic abundances determined via the analysis of recombination lines (RLs) and collisionally excited lines (CELs). We show that abundance variations can be mimicked in a {it chemically homogeneous} medium by the presence of dense X-ray irradiated regions which present different ionisation and temperature structures from those of the more diffuse medium they are embedded in, which is predominantly ionised by extreme-ultraviolet radiation. The presence of X-ray ionised dense clumps or filaments also naturally explains the lower temperatures often measured from O {sc ii} recombination lines and from the Balmer jump when compared to temperatures determined by CELs. We discuss the implications for abundances determined via the analysis of CELs and RLs and provide a simple analytical procedure to obtain upwards corrections for CEL-determined abundance. While we show that the abundance discrepancy factor (ADF) and the Balmer Jump temperature determined from observations of the Orion Nebula can simultaneously be reproduced by this model (implying upward corrections for CELs by a factor of 1.15), we find that the required X-ray fluxes exceed the known Orions stellar and diffuse X-ray budget, if we assume that the clumps are located at the edge of the blister. We propose, however, that spatially resolved observations may be used to empirically test the model, and we outline how the framework developed in this letter may be applied in the future to objects with better constrained geometries (e.g. planetary nebulae).