A systematic bias in template-based radial velocity extraction algorithms

¹ Instituto de Astrofisica e Ciências do Espaço, CAUP, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
² Departamento de Fisica e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
³ Instituto de Astrofisica e Ciências do Espaço, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁴ Département d’astronomie de l’Université de Genève, Chemin Pegasi 51, 1290 Versoix, Switzerland
⁵ University Institute of Health Sciences, CESPU, CRL, 4585-116 Gandra, Portugal
⁶ Institut Trottier de recherche sur les exoplanètes, Université de Montréal, 1375 Ave Thrèse-Lavoie-Roux, Montràl, QC H2V 0B3, Canada
⁷ Observatoire du Mont-Mégantic, Université de Montréal, Montréal H3C 3J7, Canada
⁸ Instituto de Astrofisica de Canarias, 38205 La Laguna, Tenerife, Spain
⁹ Universidad de La Laguna, Dept. Astrofisica, 38206 La Laguna, Tenerife, Spain
¹⁰ INAF - Astronomical Observatory, via Tiepolo 11, 34143 Trieste, Italy
¹¹ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
¹² Institut de Ciències de l’Espai (ICE, CSIC), Campus UAB, c/de Can Magrans s/n, 08193 Cerdanyola del Vallès, Barcelona, Spain
¹³ Institut d’Estudis Espacials de Catalunya (IEEC), Edifici RDIT, Campus UPC, 08860 Castelldefels (Barcelona), Spain
¹⁴ Departamento de Fisica, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
¹⁵ Centro de Astrobiologia (CAB), CSIC-INTA, Camino Bajo del Castillo s/n, 28692, Villanueva de la Canada, Madrid, Spain
¹⁶ Centro de Astrofisica da Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal
¹⁷ Observatoire François-Xavier Bagnoud - OFXB, 3961 Saint-Luc, Switzerland
¹⁸ INAF - Osservatorio Astrofisico di Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy
¹⁹ INAF - Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese, Italy

^★ Corresponding author.

Received: 1 April 2025
Accepted: 23 June 2025

Abstract

Context. The radial velocity (RV) method plays a key role in modern-day astrophysics. One of the most common techniques for extracting precise RVs from state-of-the-art spectrographs is template-matching (TM) algorithms. They have been shown to perform better than a cross-correlation function (CCF) approach in cases of cooler stars (e.g. M dwarfs) and multiple implementations have appeared over the past years. More recently, line-by-line (LBL) approaches offer an alternative avenue to extract RVs by analyzing individual spectral lines.

Aims. In this paper, we identify and explore a previously unidentified, multi-meter-per-second, systematic correlation between time and RVs inferred through TM and LBL methods. We evaluate the influence of the data-driven stellar template in the RV bias and hypothesise on the possible sources of this effect.

Methods. We used the s-BART pipeline to extract RVs from three different datasets gathered over four nights of ESPRESSO and HARPS observations. We demonstrate that the effect can be recovered on a larger sample of 19 targets, totalling 4124 ESPRESSO observations over 38 nights. We also showcase the presence of the bias in RVs extracted with the SERVAL and ARVE pipelines. Lastly, we explore the construction of the stellar template over the five years of ESPRESSO observations of HD 10700, totalling more than 2000 observations.

Results. We find that a systematic quasi-linear bias affects the RV extraction with slopes that vary from —0.3 ms⁻¹ h⁻¹to —52 m s⁻¹ h⁻¹ in our sample. This trend is not observed in CCF RVs and only appears when all observations of a given star are collected within a short time period (timescales of hours). We show that this systematic contamination exists in the RV time series of two different template-matching pipelines and one line-by-line pipeline, and it is agnostic to the spectrograph. We also find that this effect is linked to the construction of the stellar template, as we were able to mitigate it through a careful selection of the observations used to construct it. Our results suggest that a contamination of micro-telluric features, coupled with other sources of correlated noise, could be the driving factor of this effect. We also show that this effect does not impact the usual usage of template-matching for the detection and characterisation of exoplanets. However, the short-timescale science cases, such as asteroseismology as well as transit and atmospheric characterisation, can be severely affected.