Wavelet Transforms of Microlensing Data: Denoising, Extracting Intrinsic Pulsations, and Planetary Signals

Abstract

Wavelets are waveform functions that describe transient and unstable variations, such as noise. In this work, we study the advantages of discrete and continuous wavelet transforms (DWTs and CWTs) of microlensing data to denoise them and extract their planetary signals and intrinsic pulsations hidden by noise. We first generate synthetic microlensing data and apply wavelet denoising to them. For these simulated microlensing data with ideally Gaussian noise based on the Optical Gravitational Lensing Experiment (OGLE) photometric accuracy, denoising with DWTs reduces standard deviations of data from real models by 0.044–0.048 mag. The efficiency to regenerate real models and planetary signals with denoised data strongly depends on the observing cadence and decreases from 37% to 0.01% with increasing cadence from 15 min to 6 hr. We then apply denoising on 100 microlensing events discovered by the OGLE group. On average, wavelet denoising for these data improves standard deviations and χ n 2 of data with respect to the best-fit models by 0.023 mag and 1.16, respectively. The best-performing wavelets (based on the highest signal-to-noise ratio’s peak ( S / N max ), the highest Pearson’s correlation, or the lowest root mean squared error for denoised data) are from the Symlet and Biorthogonal wavelet families in simulated and OGLE data, respectively. In some denoised data, intrinsic stellar pulsations or small planetary like deviations appear that were covered with noise in raw data. However, through DWT denoising rather flattened and wide planetary signals could be reconstructed rather than sharp signals. CWTs and 3D frequency–power–time maps could inform about the existence of sharp signals.