Stellar rotation affects the transport of chemical elements and angular momentum and is therefore a key process during stellar evolution, which is still not fully understood. This is especially true for massive stars, which are important for the chemical enrichment of the universe. It is therefore important to constrain their physical parameters and internal angular momentum distribution to calibrate stellar structure and evolution models. Stellar internal rotation can be probed through asteroseismic studies of rotationally split oscillations but such results are still quite rare, especially for stars more massive than the Sun. The SPB star HD201433 is known to be part of a single-lined spectroscopic triple system, with two low-mass companions orbiting with periods of about 3.3 and 154 d. Our results are based on photometric observations made by BRITE - Constellation and the SMEI on board the Coriolis satellite, high-resolution spectroscopy, and more than 96 years of radial velocity measurements. We identify a sequence of 9 rotationally split dipole modes in the photometric time series and establish that HD201433 is in principle a solid-body rotator with a very slow rotation period of 297+/-76 d. Tidal interaction with the inner companion has, however, significantly accelerated the spin of the surface layers by a factor of approximately one hundred. The angular momentum transfer onto the surface of HD201433 is also reflected by the statistically significant decrease of the orbital period of about 0.9 s during the last 96 years. Combining the asteroseismic inferences with the spectroscopic measurements and the orbital analysis of the inner binary system, we conclude that tidal interactions between the central SPB star and its inner companion have almost circularised the orbit but not yet aligned all spins of the system and have just begun to synchronise rotation.
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