Synthetic Light Curve Design for Pulsating Binary Stars to Compare the Efficiency in the Detection of Periodicities

B supergiant stars pulsate in regular and quasi-regular oscillations resulting in intricate light variations that might conceal their binary nature. To discuss possible observational bias in a light curve, we performed a simulation design of a binary star affected by sinusoidal functions emulating pulsation phenomena. The Period04 tool and the WaveletComp package of R were used for this purpose. Thirty-two models were analysed based on a combination of two values on each of the k = 6 variables, such as multiple pulsations, the amplitude of the pulsation, the pulsation frequency, the beating phenomenon, the light-time effect, and regular or quasi-regular periods. These synthetic models, unlike others, consider an ARMA (1, 1) statistical noise, irregular sampling, and a gap of about 4 days. Comparing Morlet wavelet with Fourier methods, we observed that the orbital period and its harmonics were well detected in most cases. Although the Fourier method provided more accurate period detection, the wavelet analysis found it more times. Periods seen with the wavelet method have a shift due to the slightly irregular time scale used. The pulsation period hitting rate depends on the wave amplitude and frequency with respect to eclipse depth and orbital period. None of the methods was able to distinguish accurate periods leading to a beating phenomenon when they were longer than the orbital period, resulting, in both cases, in an intermediate value. When the beating period was shorter, the Fourier analysis found it in all cases except for unsolved quasi-regular periods. Overall, the Morlet wavelet analysis performance was lower than the Fourier analysis. Considering the strengths and disadvantages found in these methods, we recommend using at least two diagnosis tools for a detailed time series data analysis to obtain confident results. Moreover, a fine-tuning of trial periods by applying phase diagrams would be helpful for recovering accurate values. The combined analysis could reduce observational bias in searching binaries using photometric techniques.