The primary star in the young stellar object (YSO) binary CO Ori displays UX Ori-type variability: irregular, high amplitude optical and near-infrared photometric fluctuations where flux minima coincide with polarization maxima. This is attributed to changes in local opacity. In CO Ori A, these variations exhibit a 12.4 yr cycle. Here, we investigate the physical origin of the fluctuating opacity and its periodicity using interferometric observations of CO Ori obtained using VLTI/GRAVITY. Continuum K-band circum-primary and circum-secondary emission are marginally spatially resolved for the first time while Br$gamma$ emission is detected in the spectrum of the secondary. We estimate a spectral type range for CO Ori B of K2-K5 assuming visual extinction, $A_{rm{V}}=2$ and a distance of 430 pc. From geometric modelling of the continuum visibilities, the circum-primary emission is consistent with a central point source plus a Gaussian component with a full-width-half-maximum of 2.31$pm$0.04 milliarcseconds (mas), inclined at 30.2$pm$2.2$^{circ}$ and with a major axis position angle of 40$pm$6$^{circ}$. This inclination is lower than that reported for the discs of other UX Ori-type stars, providing a first indication that the UX Ori phenomena may arise through fluctuations in circumstellar material exterior to a disc, e.g. in a dusty outflow. An additional wide, symmetric Gaussian component is required to fit the visibilities of CO Ori B, signifying a contribution from scattered light. Finally, closure phases of CO Ori A were used to investigate whether the 12.4 yr periodicity is associated with an undetected third component, as has been previously suggested. We rule out any additional companions contributing more than 3.6% to the K-band flux within ~7.3-20 mas of CO Ori A.
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