Verification of the helioseismic Fourier-Legendre analysis for meridional flow measurements

Context. Measuring the Sun's internal meridional flow is one of the key issues of helioseismology. Using the Fourier-Legendre analysis is a technique for addressing this problem. Aims. We validate this technique with the help of artificial helioseismic data. Methods. The analysed data set was obtained by numerically simulating the e ff ect of the meridional flow on the seismic wave field in the full volume of the Sun. In this way, a 51.2-h long time series was generated. The resulting surface velocity field is then analyzed in various settings: Two 360 degrees x 90 degrees halfspheres, two 120 degrees x 60 degrees patches on the front and farside of the Sun (North and South, respectively) and two 120 degrees x 60 degrees patches on the northern and southern frontside only. We compare two possible measurement setups: observations from Earth and from an additional spacecraft on the solar farside, and observations from Earth only, in which case the full information of the global solar oscillation wave field was available. Results. We find that, with decreasing observing area, the accessible depth range decreases: the 360 degrees x 90 degrees view allows us to probe the meridional flow almost to the bottom of the convection zone, while the 120 degrees x 60 degrees view means only the outer layers can be probed. Conclusions. These results confirm the validity of the Fourier-Legendre analysis technique for helioseismology of the meridional flow. Furthermore these flows are of special interest for missions like Solar Orbiter that promises to complement standard helioseismic measurements from the solar nearside with farside observations.