Massive stars play a significant role in the chemical and dynamical evolution of galaxies. However, much of their variability, particularly during their evolved supergiant stage, is poorly understood. To understand the variability of evolved massive stars in more detail, we present a study of the O9.2Ib supergiant $zeta$ Ori Aa, the only currently confirmed supergiant to host a magnetic field. We have obtained two-color space-based BRIght Target Explorer photometry (BRITE) for $zeta$ Ori Aa during two observing campaigns, as well as simultaneous ground-based, high-resolution optical CHIRON spectroscopy. We perform a detailed frequency analysis to detect and characterize the stars periodic variability. We detect two significant, independent frequencies, their higher harmonics, and combination frequencies: the stellar rotation period $P_{mathrm{rot}} = 6.82pm0.18$ d, most likely related to the presence of the stable magnetic poles, and a variation with a period of $10.0pm0.3$ d attributed to circumstellar environment, also detected in the H$alpha$ and several He I lines, yet absent in the purely photospheric lines. We confirm the variability with $P_{mathrm{rot}}$/4, likely caused by surface inhomogeneities, being the possible photospheric drivers of the discrete absorption components. No stellar pulsations were detected in the data. The level of circumstellar activity clearly differs between the two BRITE observing campaigns. We demonstrate that $zeta$ Ori Aa is a highly variable star with both periodic and non-periodic variations, as well as episodic events. The rotation period we determined agrees well with the spectropolarimetric value from the literature. The changing activity level observed with BRITE could explain why the rotational modulation of the magnetic measurements was not clearly detected at all epochs.
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