Modelling solar radial velocities and photometric variability with SOAP

¹ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
² Departamento de Física e Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal
³ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁴ Instituto de Astrofísica e Ciências do Espaço, Department of Physics, University of Coimbra, Rua Larga, 3040-004 Coimbra, Portugal
⁵ Departamento de Ciências da Terra, FCTUC, Universidade de Coimbra, 3004-531 Coimbra, Portugal
⁶ Geophysical and Astronomical Observatory, Faculty of Science and Technology, University of Coimbra, Rua do Observatório s/n, 3040-004 Coimbra, Portugal
⁷ Department of Physics, University of Oxford, Oxford OX1 3RH, UK

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 24 October 2025
Accepted: 12 February 2026

Abstract

Context. Stellar activity remains one of the main limitations in the detection of Earth-like planets using radial velocity (RV) measurements. The Sun, as the only star for which surface features can be spatially resolved, offers a unique testbed for studying the impact of active regions on RV and photometric variability.

Aims. Using SOAPv4 (Spot Oscillation And Planet), we modelled solar RV and photometric variability induced by spots and faculae over long timescales. Our goal is to verify whether present-day, state-of-the-art models of the cross-correlation function correctly reproduce the observed variability. Moreover, we aim to assess how the choice of input data and identification technique influences the agreement between simulated and observed signals.

Methods. To simulate solar RV and photometric time series, we first identified active regions in SDO images. This was done using mathematical morphological transforms applied to SDO/HMI and AIA images. Mathematical morphological identification was validated against other state-of-the-art identification methods. Using these inputs, we ran SOAPv4 to simulate solar RVs and photometry, and we validated the results with HARPS-N RV observations, as well as with VIRGO/SPM photometric measurements.

Results. The simulations that use mathematical morphological identification achieved the best match with the observed RV time series, yielding residuals with a measured standard deviation of ~0.91 m/s. Other state-of-the-art methods produced higher filling factors and, consequently, larger discrepancies. The photometric simulations reproduced the overall variability trends.

Conclusions. We demonstrate that mathematical morphological transforms accurately identify solar active regions. Using these inputs, SOAPv4 reproduces the observed solar RV variability with a measured standard deviation of the residuals of ~0.91 m/s. Photometric simulations capture the overall variability trends, confirming that SOAP can reliably model the impact of both spots and faculae on solar RVs and photometry.