The power of wavelets in analysis of transit and phase curves in presence of stellar variability and instrumental noise I. Method and validation

Stellar photometric variability and instrumental effects, like cosmic ray hits, data discontinuities, data leaks, instrument aging etc. cause difficulties in the characterization of exoplanets and have an impact on the accuracy and precision of the modelling and detectability of transits, occultations and phase curves. This paper aims to make an attempt to improve the transit, occultation and phase-curve modelling in the presence of strong stellar variability and instrumental noise. We invoke the wavelet-formulation to reach this goal. We explore the capabilities of the software package Transit and Light Curve Modeller (TLCM). It is able to perform a joint radial velocity and light curve fit or light curve fit only. It models the transit, occultation, beaming, ellipsoidal and reflection effects in the light curves (including the gravity darkening effect, too). The red-noise, the stellar variability and instrumental effects are modelled via wavelets. The wavelet-fit is constrained by prescribing that the final white noise level must be equal to the average of the uncertainties of the photometric data points. This helps to avoid the overfit and regularizes the noise model. The approach was tested by injecting synthetic light curves into Kepler's short cadence data and then modelling them. The method performs well over a certain signal-to-noise (S/N) ratio. In general a S/N ratio of 10 is needed to get good results but some parameters requires larger S/N, some others can be retrieved at lower S/Ns. We give limits in terms of signal-to-noise ratio for every studied system parameter which is needed to accurate parameter retrieval. The wavelet-approach is able to manage and to remove the impacts of data discontinuities, cosmic ray events, long-term stellar variability and instrument ageing, short term stellar variability and pulsation and flares among others. (...)