Detection of low-level periodic signals through enhanced self-correlation method. The case of ER Vulpeculae

• Published in: Monthly notices of the Royal Astronomical Society Vol. 448; no. 3; pp. 2066 - 2076
• Main Authors: Crăciun, Maria, Vamoş, Călin, Pop, Alexandru
• Format: Journal Article
• Language: English
• Published: London Oxford University Press 11.04.2015
• Subjects: Astronomy; Binary system; Computer simulation; Confidence intervals; Electric noise; Fourier analysis; Mathematical analysis; Mathematical models; Monte Carlo methods; Monte Carlo simulation; Orbitals; Sampling; Seismology; Time series; methods: statistical; methods: data analysis; stars: individual: ER Vulpeculae
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stv108

The self-correlation (SC) method proposed three decades ago by Percy, Jakate and Matthews is a complementary time series analysis method which provides a characterization of a variability phenomenon and an estimation of the involved time-scale. It can be applied to periodic, quasi-periodic and irregular phenomena, for either evenly or unevenly sampled data. An important deficiency of this method – mentioned by Percy himself – is the fact that the statistical properties of the SC are unknown so that the statistical significance of an ‘observed’ (quasi-)periodicity cannot be estimated. In this paper, we investigate analytically and numerically the properties of the SC of a harmonic periodic signal by taking into account the influence of the finite length of the data set, the non-equidistant sampling, and the presence of an additive Gaussian white noise. This method is used to investigate the already inferred periodic modulation of the orbital period of the eclipsing binary system ER Vul. In addition, we propose an improvement of the SC method by applying the ‘stacking method’ already used in seismology, which we call the enhanced SC (ESC) method. A statistical test relying on the ESC method together with Monte Carlo simulations allow us to claim the presence of a deterministic component at a significantly higher confidence level than that obtained through a Fourier based method. The evaluation of the detectability of the ER Vul periodic phenomenon through the ESC method provides similar results as those previously obtained using the Fourier based method.