A Comprehensive Method to Measure Solar Meridional Circulation and the Center-to-limb Effect Using Time-Distance Helioseismology

Meridional circulation is a crucial component of the Sun's internal dynamics, but its inference in the deep interior is complicated by a systematic center-to-limb effect in helioseismic measurement techniques. Previously, an empirical method, removing travel-time shifts measured for the east-west traveling waves in the equatorial area from those measured for the north-south traveling waves in the central meridian area, was used, but its validity and accuracy need to be assessed. Here, we develop a new method to separate the center-to-limb effect, delta tau(CtoL), and the meridional-flow-induced travel-time shifts, delta tau(MF), in a more robust way. Using 7-year observations of the Solar Dynamics Observatory/Helioseismic and Magnetic Imager, we exhaustively measure the travel-time shifts between two surface locations along the solar disk's radial direction for all azimuthal angles and all skip distances. The measured travel-time shifts are a linear combination of dtCtoL and dtMF, which can be disentangled by solving the linear equation set. The delta tau(CtoL) is found to be isotropic relative to the azimuthal angle, and the delta tau(MF) is then inverted for the meridional circulation. Our inversion results show a three-layer flow structure, with equatorward flow found between about 0.82 and 0.91 R-circle dot for low latitude areas and between about 0.85 and 0.91 R-circle dot for higher latitude areas. Poleward flows are found below and above the equatorward flow zones, indicating a double-cell circulation in each hemisphere.