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

Abstract

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 effect 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• × 90• halfspheres, two 120• × 60• patches on the front and farside of the Sun (North and South, respectively) and two 120• × 60• 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• × 90• view allows us to probe the meridional flow almost to the bottom of the convection zone, while the 120• × 60• 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.

Inversions for Deep Solar Meridional Flow Using Spherical Born Kernels

“…In addition, there are several efforts underway to de-vboening@leibniz-kis.de velop or validate new methods for inferring the meridional flow, in particular using local helioseismic techniques (e.g., Böning et al 2016;Roth et al 2016;Gizon et al 2017).…”

Probing the Solar Meridional Circulation using Fourier Legendre Decomposition

“…Longer-lived "global" modes, typically at low degrees and low frequencies, show isolated peaks, whose frequencies are not affected to first order by meridional flow (Gough & Hindman 2010). The "frequency shifts" which can be measured in this mode regime through FLD methods result from a redistribution of power, through mode coupling produced by advection, between modes of nearby degree and which leak into the observed spectra (Roth et al 2016). Our determination of frequency shifts is discussed further in §3.…”

“…In that study, we applied the method now known as Fourier Legendre decomposition (hereafter FLD) to one month of GONG data and 8 days of Dopplergrams from the Michelson Doppler Imager (MDI) instrument (Scherrer et al 1995) onboard the Solar and Heliospheric Observatory. With various modifications, the FLD method has been employed in a number of subsequent studies of solar meridional circulation (Krieger et al 2007;Doerr et al 2010) as well as undergone development and validation studies (Roth et al 2016;Hecht & Roth 2018). We note that the method used by Mitra-Kraev & Thompson (2007) is closely related to FLD analysis, but applied selectively to waves propagating along the central meridian.…”

The Solar Orbiter mission

“…Howe et al 2015), the meridional flow (e.g. Roth et al 2016;Komm et al 2018 Observations by Hinode's Solar Optical Telescope (SOT, Tsuneta et al 2008a) have already provided a glimpse of the Sun's high-latitude region above 70 • (see Tsuneta et al 2008b;Petrie 2017) by making use of the Sun's B 0 angle of 7 • . However, in general, observations from outside the ecliptic plane are required to reliably measure the Sun's time-dependent surface magnetic field near the poles.…”