New Insights into Time Series Analysis III: Setting constraints on period analysis

Abstract

E-science of photometric data requires automatic procedures and a precise recognition of periodic patterns to perform science as well as possible on large data. Analytical equations that enable us to set the best constraints to properly reduce processing time and hence optimize signal searches play a crucial role in this matter. These are increasingly important because the production of unbiased samples from variability indices and statistical parameters has not been achievable so far. We discuss the constraints used in periodic signals detection methods as well as the uncertainties in the estimation of periods and amplitudes. The frequency resolution necessary to investigate a time series is assessed with a new approach that estimates the necessary sampling resolution from shifts on the phase diagrams for successive frequency grid points.We demonstrate the underlying meaning of the oversampling factor. We reassess the frequency resolutions required to find the variability periods of EA stars and use the new resolutions to analyse a small sample of EA up Catalina stars, i.e. EA stars previously classified as having insufficient number of observations at the eclipses. As a result, the variability periods of four EA up stars were determined. Moreover, we have a new approach to estimate the amplitude and period variations. From these estimations information about the intrinsic variations of the sources are obtained. For a complete characterization of the light curve signal the period uncertainty and period variation must be determined. Constraints on periodic signal searches were analysed and delimited.

Recovering variable stars in large surveys: EAup Algol-type class in the Catalina Survey

“…For unevenly spaced data, as is the case for most of the present surveys, we face an additional difficulty: the Nyquist frequency, f Ny , has not a precise definition anymore, and the frequency grid is consequently not well defined as well. Ferreira Lopes et al (2018) derived an expression (see equation 1) that parametrizes the frequency resolution in terms of an oversampling factor with respect to the ideal, equally spaced times series case. The number of frequencies N f is given by…”

“…Although the number of catalogued EAs is fairly large, the observational strategies in the surveys vary a lot, and the methodologies for finding periods may fail in cases having narrow eclipses or few data points during these events. Ferreira Lopes, Cross & Jablonski (2018) discussed the influence of the resolution of the frequency grid in the search for periodicities in EAs. They have succeeded in finding periods for four objects previously identified by Drake et al (2014) as having insufficient number of observations in the eclipses.…”

“…This work is the first of a series in an attempt to determine the periods of EAs having narrow eclipses adopting the methodology proposed by Ferreira Lopes et al (2018). Here we focus on EAs from CRTS with unknown period (EA up class).…”

VVV survey near-infrared colour catalogue of known variable stars

“…The VIVA catalogue (Ferreira Lopes et al 2020) is based on a variability analysis of the VVV-DR4 Data Release that is the same as we used here. It was compiled following a series of recommendations in the New Insight into Time Series Analysis (NITSA -Ferreira Lopes & Cross 2016b, 2017bFerreira Lopes et al 2018). These criteria provide a good prescription for select-Herpich et al: VVV survey near-infrared colour catalogue of known variable stars Fig.…”

New type II Cepheids from VVV data towards the Galactic center

“…As a matter of fact, Df = ∆t −1 is the characteristic width of a peak in the periodogram. Therefore, we set N f req = int(n spp · ∆t · (ν max − ν min )), where n spp is the oversampling factor (Graham et al 2013) and n spp corresponds to a phase shift of about 0.1 between neighboring frequencies that ensure the signal detection of almost all variable types (for more detail see Ferreira Lopes et al 2018). We set n spp = 9 for all the light curves (normally, the recommended value of n spp is between 5 and 10; VanderPlas & Ivezić 2015).…”