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

II. Accuracy of the transit parameters

¹ MTA-ELTE Exoplanet Research Group, 9700, Szent Imre h. u. 112, Szombathely, Hungary
² ELTE Eötvös Loránd University, Doctoral School of Physics, 1117 Budapest, Pázmány Péter sétány 1/A, Hungary
e-mail: xilard1@gothard.hu
³ Konkoly Observatory, Research Centre for Astronomy and Earth Sciences, Eötvös Loránd Research Network (ELKH), Konkoly-Thege Miklós út 15-17, 1121 Budapest, Hungary
⁴ CSFK, MTA Centre of Excellence, Konkoly Thege Miklós út 15-17, 1121 Budapest, Hungary
⁵ ELTE Eötvös Loránd University, Gothard Astrophysical Observatory, Szent Imre h. u. 112, 9700 Szombathely, Hungary
⁶ MTA-ELTE Lendület “Momentum” Milky Way Research Group, Szent Imre h. u. 112, 9700 Szombathely, Hungary
⁷ Deutsches Zentrum für Luft- und Raumfahrt, Institute of Planetary Research, Rutherfordtstrasse 2, 12489 Berlin, Germany

Received: 30 December 2021
Accepted: 25 April 2023

Abstract

Context. Correlated noise in exoplanet light curves, such as noise from stellar activity, convection noise, and instrumental noise, distorts the exoplanet transit light curves and leads to biases in the best-fit transit parameters. An optimal fitting algorithm can provide stability against the presence of correlated noises and lead to statistically consistent results, namely, the actual biases are usually within the error interval. This is not automatically satisfied by most of the algorithms in everyday use and the testing of the algorithms is necessary.

Aims. In this paper, we describe a bootstrapping-like test to handle with the general case and we apply it to the wavelet-based Transit and Light Curve Modeller (TLCM) algorithm, testing it for the stability against the correlated noise. We compare and contrast the results with regard to the FITSH algorithm, which is based on an assumption of white noise.

Methods. We simulated transit light curves with previously known parameters in the presence of a correlated noise model generated by an Autoregressive Integrated Moving Average (ARIMA) process. Then we solved the simulated observations and examined the resulting parameters and error intervals.

Results. We have found that the assumption of FITSH, namely, that only white noise is present, has led to inconsistencies in the results: the distribution of best-fit parameters is then broader than the determined error intervals by a factor of 3–6. On the other hand, the wavelet-based TLCM algorithm handles the correlated noise properly, leading to both properly determined parameter and error intervals that are perfectly consistent with the actual biases.