Power of wavelets in analyses of transit and phase curves in the presence of stellar variability and instrumental noise

I. Method and validation

¹ Deutsches Zentrum für Luft- und Raumfahrt, Institute of Planetary Research, Rutherfordtstrasse 2, 12489 Berlin, Germany
e-mail: szilard.csizmadia@dlr.de
² ELKH-SZTE Stellar Astrophysics Research Group, 6500 Baja, Szegedi út Kt. 766, Hungary
³ Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, ELKH, Konkoly-Thege Miklós út. 1121, Hungary
⁴ MTA-ELTE Exoplanet Research Group, Szombathely, Szent Imre h. u. 112, 9700, Hungary
⁵ ELTE Eötvös Loránd University, Doctoral School of Physics, Budapest, Pázmány Péter sétány 1/A, 1117, Hungary
⁶ CSFK, MTA Centre of Excellence, Budapest, Konkoly Thege Miklós út 15-17, 1121, Hungary
⁷ Department of Physics and Astronomy, University of California, Irvine, 4129 Frederick Reines Hall, Irvine, CA 92697, USA

Received: 13 May 2021
Accepted: 25 April 2023

Abstract

Context. Stellar photometric variability and instrumental effects, such as cosmic ray hits, data discontinuities, data leaks, instrument aging, and so on, lead to difficulties in the characterisation of exoplanets. Therefore, they can impact the accuracy and precision of the modelling and the detectability of their transits, occultations, and phase curves.

Aims. This paper is aimed at improving the transit, occultation, and phase-curve modelling in the presence of strong stellar variability and instrumental noise. To this end, we invoke the wavelet formulation.

Methods. We explored the capabilities of the software package Transit and Light Curve Modeller (TLCM). It is able to perform (1) a joint radial-velocity and light-curve fit or (2) a light curve-only fit. It models the transit, occultation, beaming, ellipsoidal, and reflection effects in the light curves (including the gravity-darkening effect). Here, the red noise, stellar variability, and instrumental effects were modelled via wavelets. The wavelet fit was 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 overfitting and regularises the noise model. The approach was tested by injecting synthetic light curves into short-cadence Kepler data and modelling them.

Results. The method performs well over a certain signal-to-noise (S/N) ratio. We provide limits in terms of the S/N for every studied system parameter that is needed for accurate parameter retrieval. The wavelet approach is able to manage and remove the impact of data discontinuities, cosmic ray events, and long-term stellar variability and instrument ageing, as well as short-term stellar variability, pulsation, and flares (among others).

Conclusions. We conclude that precise light-curve models combined with the wavelet method and with well-prescribed constraints on the white noise are able to retrieve the planetary system parameters, even in the presence of strong stellar variability and instrumental noise, including data discontinuities.