Precise and efficient modeling of stellar-activity-affected solar spectra using SOAP-GPU

Context. One of the main obstacles in exoplanet detection when using the radial velocity (RV) technique is the presence of stellar activity signal induced by magnetic regions. As the most advanced techniques to mitigate this signal are reaching a level better than one meter per second, it is difficult to evaluate their performance: instrumental systematics start to be similar in magnitude, and therefore it is impossible to know the ground truth of the stellar activity signal. In this context, a realistic simulated dataset that can provide photometry and spectroscopic outputs is needed for method development. Aims. The goal of this paper is to describe two realistic simulations of solar activity obtained from SOAP-GPU and to compare them with real data obtained from the HARPS-N solar telescope. For this purpose, both simulated spectral time series cover the time window of HARPS-N solar observation, but nothing prevents SOAP-GPU from modeling the data over different time spans. Methods. We describe two different methods of modeling solar activity using SOAP-GPU. The first models the evolution of active regions based on the spot number as a function of time. Other physical parameters are either drawn from observed solar distributions or modeled with empirical relations. The second method relies on the extraction of active regions from the Solar Dynamics Observatory (SDO) data. The location of spots and faculae on the solar disk at each timestamp are derived from the magnetogram and intensity maps and are fed into SOAP-GPU to simulate the corresponding spectra. Results. The simulated spectral time series generated with the first method shows a long-term RV behavior similar to that seen in the HARPS-N solar observations. The effect of stellar activity induced by stellar rotation is also well modeled with prominent periodicities at the stellar rotation period and its first harmonic. The comparison between the simulated spectral time series generated using SDO images and the HARPS-N solar spectra shows that SOAP-GPU can precisely model the RV time series of the Sun to a precision better than 0.9 m/s. By studying the width and depth variations of each spectral line in the HARPS-N solar and SOAP-GPU data, we find a strong correlation between the observation and the simulation for strong spectral lines, therefore supporting the modeling of the stellar activity effect at the spectral level. The correlations are weaker for shallow lines, although it is likely that their lower signal-to-noise ratio does not allow a meaningful comparison. Conclusions. We introduce two methods for modeling solar activity using SOAP-GPU. With only sunspot numbers as input, we accurately capture the long-term magnetic cycle and rotational features. Additionally, we effectively model shift and depth variations at the spectral line level by using data from SDO. These simulated solar spectral time series serve as a useful test bed for evaluating spectral-level stellar activity mitigation techniques.