Wavelets: a powerful tool for studying rotation, activity, and pulsation inKeplerand CoRoT stellar light curves

Abstract

Aims. The wavelet transform has been used as a powerful tool for treating several problems in astrophysics. In this work, we show that the time-frequency analysis of stellar light curves using the wavelet transform is a practical tool for identifying rotation, magnetic activity, and pulsation signatures. We present the wavelet spectral composition and multiscale variations of the time series for four classes of stars: targets dominated by magnetic activity, stars with transiting planets, those with binary transits, and pulsating stars. Methods. We applied the Morlet wavelet (6th order), which offers high time and frequency resolution. By applying the wavelet transform to the signal, we obtain the wavelet local and global power spectra. The first is interpreted as energy distribution of the signal in time-frequency space, and the second is obtained by time integration of the local map. Results. Since the wavelet transform is a useful mathematical tool for nonstationary signals, this technique applied to Kepler and CoRoT light curves allows us to clearly identify particular signatures for different phenomena. In particular, patterns were identified for the temporal evolution of the rotation period and other periodicity due to active regions affecting these light curves. In addition, a beat-pattern signature in the local wavelet map of pulsating stars over the entire time span was also detected.

THE ROTATION PERIOD DISTRIBUTIONS OF 4–10 Myr T TAURI STARS IN ORION OB1: NEW CONSTRAINTS ON PRE-MAIN-SEQUENCE ANGULAR MOMENTUM EVOLUTION

“…We applied the Generalized Lomb-Scargle Periodogram (GLS; Zechmeister & Kürster 2009) and the Multiband Periodogram (VanderPlas & Ivezić 2015) to calculate the probable periods, the uncertainty formula described by Kovacs (1981) to calculate the uncertainties in periods, and the Baluev method (Baluev 2008) to calculate the False Alarm Probability (FAP). We also used the Wavelet transform method (Bravo et al 2014) to determine the probable periods for stars with conflicting periods. All of these methods were combined into a single pipeline, shown in Figure 2, that provides the most likely period for each time-series while reducing the effect of bias.…”

“…We used the Morlet Wavelet Transform method 3 (Bravo et al 2014) to search for periods of certain stars. The wavelet transform method takes the time series as input and generates a two-dimensional period vs. time plot.…”

The Astrophysics of Visible-light Orbital Phase Curves in the Space Age

“…Therefore, identifying this false positive scenario requires looking for changes in the periodic signal over time. This can be done for example by comparing results from different subsets of the data or using a wavelet-based approach (Bravo et al 2014). Since the level of activity depends on the star's convective layer size this false positive scenario is expected to occur for M to late-F type stars and not likely to occur for early-F type and hotter stars.…”

THE ROTATIONAL BEHAVIOR OFKEPLERSTARS WITH PLANETS

“…Accordingly, in each periodogram, we identified the main peak with a confidence level of greater than 99%. We also computed wavelet maps and global wavelet power spectra within the same frequency range that was used for the Lomb-Scargle periodograms, following the procedure described in Bravo et al (2014). These authors treated the 6 th -order Morlet wavelet as the mother wavelet, because of its good time localization and frequency resolution (Grossmann & Morlet 1984).…”

“…In addition, Bravo et al (2014) performed an unprecedented comparison of different variability signatures in wavelet maps, including rotational modulation. This approach was also considered in our visual inspection procedure for better identification photometric variability induced by spots.…”