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Classical Be stars, regardless of spectral subtype, display multiperiodiclight modulations in the frequency range 0.1-12 d$^{-1}$, when observed withhigh-cadence and long duration. This behaviour is attributed to non-radialpulsations and/or rotation of the Be star. The main goal of this work is toinvestigate the fast photometric variability of the optical counterparts toBe/X-ray binaries and compare the general patterns of such variability with theGalactic population of classical Be stars. We analyzed 21 sources with TESS.High-cadence photometry with two ground-based telescopes was also performed for15 sources. Standard Fourier analysis and least-squares fitting methods wereemployed in the frequency analysis. All sources exhibit intra-night lightvariations with intensity variations of 0.01-0.06 mag in the ground-basedobservations and up to 5% in flux in TESS observations. This variabilitymanifests itself as multi-periodic signals in the frequency range 0.2-12d$^{-1}$. We find that the patterns of variability of the Be stars in Be/X-raybinaries agree with that of classical early-type Be stars in terms of thegeneral shape of the periodograms. Based on the general shape and number ofpeaks in the periodograms, Be/X-ray binaries can be classified into differenttypes. The most common case is the presence of groups of closely-spacedfrequencies (67%), followed by sources that exhibit isolated signals (18%). Theremaining type of sources displays frequency spectra characterized by a mixedpattern of stochastic variability and high-frequency peaks. This study revealsthat short-term optical photometric variability is a very common, if notubiquitous, feature intrinsic to the Be optical companions in Be/X-raybinaries. This variability is mainly attributed to pulsations that originate inthe stellar interior.

Fast time optical variability in Be/X-ray binaries. Pulsation and rotation