Top panel: periodogram of the simulated radial velocity time series of the Sun as a star with sectoral r modes with m = 2 and m = 3 as seen by anEarth observer. The RV maximum amplitude of the m = 2 mode is 24.5 cm s−1, while the amplitude of the m = 3 mode is 7.1 cm s−1; the periods of the modes are given in the text. These RV amplitudes correspond to a maximum horizontal velocity of the modes of 2 ms−1 at the surface of the Sun. The periodogram of a noiseless time series is plotted with a thin blue solid line, while the periodogram obtained adding a normally distributed random noise with a standard deviation σn = 10 cm s−1 is plotted with the thicker green solid line. The vertical dashed line indicates the period of the m = 2 mode and the dotted line that of the m = 3 mode, if the inclination B0 of the solar equator is fixed. The red horizontal line indicates the level of 1% FAP. Bottom panel: same as the top panel, but the maximum RV amplitude of the sectoral m = 2 mode is now assumed to be 8.2 cm s−1, corresponding to the upper limit for the amplitude of this mode found by Liang et al. (2018), while the amplitude of the m = 3 mode is still 7.1 cm s−1. The upper limit for the m = 2 mode corresponds to a maximum horizontal velocity of 0.7 m s−1 at the surface of the Sun.
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