Calculation of period of δ Scuti stars using generalized Lomb-Scargle periodogram technique

Astronomical observations are usually sparse and non-uniform, sometimes contaminated with random or systematic noises. They always packed in certain time periods (nights) separated by several hours or maybe days. Fourier analysis which regularly used to analyze periodicities in time series could not be implemented in astronomical time series because it generates fake signals in power spectrum. Lomb-Scargle periodogram is a well-known algorithm to detect periodicities in a set of non-uniformly spaced data. This method implements least-squares fitting of sine and cosine waves in form of  and search for best fitted frequencies. It is suitable for time series with zero mean. The significance of the detected periods is inferred by comparing power of the signal with a random estimation of false alarm probability (FAP). In this paper, we manipulate the generalized Lomb-Scargle periodogram (GLS) to calculate periods for a typical δ Scuti star. The GLS is an extension to the Lomb-Scargle periodogram which takes into account the measurement of errors and also is more suitable for time series with non-zero average. GLS tries to fit the equation  to the time series and find the power spectrum for frequencies. We consider a given periodogram peak, derived from GLS, significant when it exceeds the one present “false alarm probability” level (FAP), which means there is 99% confidence that it is real and could not be simulated by Gaussian noise. FAP levels are calculated by performing random permutations of the data with similar times of observations. δ Scuti variable stars lie in the lower part of the instability strip on the main sequence in Hertzprung-Rassell diagram with luminosity classes between III to V. They are belonging to the disc population and usually are not observed in globular clusters. The variability of this type of stars was discovered in 1963 and was assigned to the group of irregular variables. They are obeying a period-luminosity relation like cepheids and can be used as standard candles. Their pulsating period is less than 1 day. Many of these stars show multiple periods with amplitudes less than 0.1 mag. These stars pulsate in radial and non-radial modes and are important as their pulsations can be used as tracer of their internal structures. We implement the generalized Lomb-Scargle periodogram to detect period for high amplitude variable star BS Aqr (HD223338) which is a δ Scuti of A8 III spectral type with very short period (0.01-0.2 days) and low amplitudes (less than 0.9 mag) and almost sinusoidal light curves. Different interpretations are given in the literature about the nature of variability for this star. Its period is continuously decreasing. Most authors have agreed with the monoperiodic nature of this star. Using photometric data taken in La Silla Observatory that covered 30 September to 6 November 1983, we find that BS Aqr is an monoperiodic δ Scuti and detect a period of 0.1977 days for the star pulsation. The result is in good agreement with pervious results from this star which demonstrates the capability of the Generalized Lomb-Scargle method to study brightness variation in variable stars.