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We report on the numerical discovery of quasi‐periodic oscillations (QPOs) associated with accretion through a non‐axisymmetric magnetic boundary layer in the unstable regime, when two ordered equatorial streams form and rotate synchronously at approximately the angular velocity of the inner disc. The streams hit the star's surface producing hotspots. Rotation of the spots leads to high‐frequency QPOs. We performed a number of simulation runs for different magnetospheric sizes from small to tiny, and observed a definite correlation between the inner disc radius and the QPO frequency: the frequency is higher when the magnetosphere is smaller. In the stable regime, a small magnetosphere forms and accretion through the usual funnel streams is observed, and the frequency of the star is expected to dominate the light curve. We performed exploratory investigations of the case in which the magnetosphere becomes negligibly small and the disc interacts with the star through an equatorial belt. We also performed investigation of somewhat larger magnetospheres where one or two ordered tongues may dominate over other chaotic tongues. In application to millisecond pulsars, we obtain QPO frequencies in the range of 350–990 Hz for one spot. The frequency associated with rotation of one spot may dominate if spots are not identical or antipodal. If the spots are similar and antipodal, then the frequencies are twice as high. We show that variation of the accretion rate leads to drift of the QPO peak.

Discovery of drifting high‐frequency quasi‐periodic oscillations in global simulations of magnetic boundary layers