OB stars are important constituents for the ecology of the Universe, and there are only a few studies on their pulsational properties detailed enough to provide important feedback on current evolutionary models. Our goal is to analyse and interpret the behaviour present in the CoRoT light curve of the B0.5 IV star HD 51756 observed during the second long run of the space mission, and to determine the fundamental stellar parameters from ground-based spectroscopy gathered with the CORALIE and HARPS instruments after checking for signs of variability and binarity, thus making a step further in mapping the top of the Beta Cep instability strip. We compare the newly obtained high-resolution spectra with synthetic spectra of late O-type and early B-type stars computed on a grid of stellar parameters. We match the results with evolutionary tracks to estimate stellar parameters. We use various time series analysis tools to explore the nature of the variations present in the light curve. Additional calculations are carried out based on distance and historical position measurements of the components to impose constraints on the binary orbit. We find that HD 51756 is a wide binary with both a slow (v sin i approx 28 km s^-1) and a fast (v sin i approx 170 km s^-1) early-B rotator whose atmospheric parameters are similar (T_eff approx 30000 K and log g approx 3.75). We are unable to detect pulsation in any of the components, and we interpret the harmonic structure in the frequency spectrum as sign of rotational modulation, which is compatible with the observed and deduced stellar parameters of both components. The non-detection of pulsation modes provides a feedback on the theoretical treatment, given that non-adiabatic computations applied to appropriate stellar models predict the excitation of both pressure and gravity modes for the fundamental parameters of this star.
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