Stellar activity induced by active structures (eg, spots, faculae) is known to strongly impact the radial velocity time series. It then limits the detection of small planetary RV signals (eg, an Earth-mass planet in the habitable zone of a solar-like star). In previous papers, we studied the detectability of such planets around the Sun seen as an edge-on star. For that purpose, we computed the RV and photometric variations induced by solar magnetic activity, using all active structures observed over one entire cycle. 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 forthcoming instruments. 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 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 for a `Sun seen with various inclinations. The produced RV signal takes into account the photometric contribution of structures as well as the attenuation of the convective blueshift. The comparison between our simulated activity pattern and the observed one validates our model. We show that the inclination of the stellar rotation axis has a significant impact on the time series. RV long-term amplitudes as well as short-term jitters are significantly reduced when going from edge-on to pole-on configurations. Assuming spin-orbit alignment, the optimal configuration for planet detection is an inclined star (i~45{deg}).
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