Like other young stellar objects (YSOs), FU Ori-type stars have been detected as strong X-ray emitters. However, little is known about how the outbursts of these stars affect their X-ray properties. We assemble available X-ray data from XMM Newton and Chandra observations of 16 FU Ori stars, including a new XMM Newton observation of Gaia 17bpi during its optical rise phase. Of these stars, six were detected at least once, while 10 were non-detections, for which we calculate upper limits on intrinsic X-ray luminosity ($L_X$) as a function of plasma temperature ($kT$) and column density ($N_H$). The detected FU Ori stars tend to be more X-ray luminous than typical for non-outbursting YSOs, based on comparison to a sample of low-mass stars in the Orion Nebula Cluster. FU Ori stars with high $L_X$ have been observed both at the onset of their outbursts and decades later. We use the Kaplan-Meier estimator to investigate whether the higher X-ray luminosities for FU Ori stars is characteristic or a result of selection effects, and we find the difference to be statistically significant ($p<0.01$) even when non-detections are taken into account. The additional X-ray luminosity of FU Ori stars relative to non-outbursting YSOs cannot be explained by accretion shocks, given the high observed plasma temperatures. This suggests that, for many FU Ori stars, either 1) the outburst leads to a restructuring of the magnetosphere in a way that enhances X-ray emission, or 2) FU Ori outbursts are more likely to occur among YSOs with the highest quiescent X-ray luminosity.
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