Using the Sun to estimate Earth-like planets detection capabilities V. Parameterizing the impact of solar activity components on radial velocities

Context. Stellar activity induced by active structures such as stellar spots and faculae is known to have a strong impact on the radial velocity (RV) time series. It is therefore a strong limitation to the detection of small planetary RV signals, such as that of an Earth-mass planet in the habitable zone of a solar-like star. In a series of previous papers, we have studied the detectability of such planets around the Sun observed as a star in an edge-on configuration. For this purpose, we computed the RV, photometric and astrometric variations induced by solar magnetic activity, using all active structures observed over one entire cycle. Aims. Our goal is to perform similar studies on stars with different physical and geometrical properties. As a first step, we focus on Sun-like stars seen with various inclinations, and on estimating detection capabilities with future instruments. Methods. To do so, we first parameterize the solar active structures with the most realistic pattern so as to obtain results consistent with the observed ones. We simulate the growth, evolution and decay of solar magnetic features (spots, faculae and network), using parameters and empiric laws derived from solar observations and literature. We generate the corresponding structure lists over a full solar cycle. We then build the resulting spectra and deduce the RV and photometric variations, first in the case of a sun seen edge-on and then with various inclinations. The produced RV signal takes into account the photometric contribution of spots and faculae as well as the attenuation of the convective blueshift in faculae. We then use these patterns to study solar-like stars with various inclinations. Results. The comparison between our simulated activity pattern and the observed pattern validates our model. We show that the inclination of the stellar rotation axis has a significant impact on the photometric and RV time series. Radial velocity long-term amplitudes and short-term jitters are significantly reduced when going from edge-on to pole-on configurations. Assuming spin-orbit alignment, the best configuration for planet detection is an inclined star (i similar or equal to 45 degrees).