Accounting for stellar activity signals in radial-velocity data by using change point detection techniques^★

¹ Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
e-mail: umberto.simola@gmail.com
² Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria
e-mail: andrea.bonfanti@oeaw.ac.at
³ Observatoire de Genève, Université de Genève, 51 ch. des Maillettes, 1290 Versoix, Switzerland
⁴ Department of Statistics, University of Wisconsin – Madison, USA
⁵ Department of Computer Science, Aalto University, Espoo, Finland
⁶ Department of Biostatistics, University of Oslo, Oslo, Norway

Received: 17 December 2021
Accepted: 20 May 2022

Abstract

Context. Active regions on the photosphere of a star have been the major obstacle for detecting Earth-like exoplanets using the radial velocity (RV) method. A commonly employed solution for addressing stellar activity is to assume a linear relationship between the RV observations and the activity indicators along the entire time series, and then remove the estimated contribution of activity from the variation in RV data (overall correction method). However, since active regions evolve on the photosphere over time, correlations between the RV observations and the activity indicators will correspondingly be anisotropic.

Aims. We present an approach that recognizes the RV locations where the correlations between the RV and the activity indicators significantly change in order to better account for variations in RV caused by stellar activity.

Methods. The proposed approach uses a general family of statistical breakpoint methods, often referred to as change point detection (CPD) algorithms; several implementations of which are available in R and python. A thorough comparison is made between the breakpoint-based approach and the overall correction method. To ensure wide representativity, we use measurements from real stars that have different levels of stellar activity and whose spectra have different signal-to-noise ratios.

Results. When the corrections for stellar activity are applied separately to each temporal segment identified by the breakpoint method, the corresponding residuals in the RV time series are typically much smaller than those obtained by the overall correction method. Consequently, the generalized Lomb–Scargle periodogram contains a smaller number of peaks caused by active regions. The CPD algorithm is particularly effective when focusing on active stars with long time series, such as α Cen B. In that case, we demonstrate that the breakpoint method improves the detection limit of exoplanets by 74% on average with respect to the overall correction method.

Conclusions. CPD algorithms provide a useful statistical framework for estimating the presence of change points in a time series. Since the process underlying the RV measurements generates anisotropic data by its intrinsic properties, it is natural to use CPD to obtain cleaner signals from RV data. We anticipate that the improved exoplanet detection limit may lead to a widespread adoption of such an approach. Our test on the HD 192310 planetary system is encouraging, as we confirm the presence of the two hosted exoplanets and we determine orbital parameters consistent with the literature, also providing much more precise estimates for HD 192310 c.