Diving into the magnetosphere of the Of?p star HD 108

We analyse optical and X-ray spectroscopy of the Of?p star HD 108, known for its strong dipolar magnetic field and its optical line profile variability with a time-scale of 54 +/- 3 yrs, interpreted as the stellar rotation period. Optical emission lines have now recovered from their minimum emission state reached in 2007-2008. The variations of the equivalent width of the H alpha emission provide constraints on the inclination of the rotation axis (i) and the obliquity of the magnetic axis (beta). The best agreement between model and observations is found for (i, beta) pairs with i + beta similar or equal to 85 degrees and i is an element of[30 degrees, 55 degrees]. The Balmer emission lines display stochastic variability at the similar to 5 per cent level on time-scales of a few days. TESS photometry unveils transient modulations on similar time-scales in addition to prominent red noise variations. A Chandra X-ray observation of December 2021, when the star was at a higher emission level, indicates a slight increase of the flux and a spectral hardening compared to the August 2002 XMM-Newton observation, taken near minimum emission state. Magnetohydrodynamic simulations are used to compute synthetic X-ray spectra. With our current best estimate of the M-B=0 mass-loss rate, the simulated X-ray luminosity and spectral energy distribution agree very well with the observations. Finally, the radial velocities vary on a period of 8.5 yr with a peak-to-peak amplitude of 10-11 km s(-1), suggesting orbital motion with an unseen companion of at least 4 M-circle dot.