Modelling solar radial velocities and photometric variability with SOAP

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.